Fernandez will miss the FA Cup quarter-final tie on Saturday against Port Vale and next Sunday's Premier League clash with Manchester City, live on Sky Sports.
But Rosenior revealed no disciplinary action would be taken against Marc Cucurella after he criticised the club's recruitment policy and questioned Enzo Maresca's exit in an interview over the international break.
"It's disappointing to speak in that way. What I will say about Enzo is that, in terms of him as a person, I've got no bad words to say," Rosenior said at his press conference on Friday.
"But a line was crossed in terms of our culture. We had to make a sanction."
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Fernandez has been regularly linked with a summer move to Real and he cast doubt over his Chelsea future after their heavy Champions League last-16 defeat to Paris Saint-Germain, telling ESPN Argentina "I don't know" when asked if he would still be at the club next season.
"My focus is here now. Then the World Cup coming up, so we'll see after that," he added.
Fernandez went further during his time with Argentina in the international break, telling Marcos Giles, an Argentine media personality, "I really like Madrid - it's similar to Buenos Aires".
Fernandez was then questioned on whether he would consider living in Madrid, saying: "Yes, of course."
Rosenior added on Fernandez: "Firstly, as a character, a person and a player, I have the utmost respect for Enzo Fernandez for what he's achieved in his career.
"He's frustrated because he wanted Chelsea to be successful this year. He still wants that, and we still can be.
"In terms of the decision, we are aligned in every decision that we make, so it was a joint decision.
"The door is not closed on Enzo - that's very important. It's a sanction. You have to protect this club and culture, and in terms of that, the line was crossed in the international break."
Merse criticises decision to drop Fernandez
Paul Merson speaking on Soccer Special:
"I think Enzo has sat down with him [Rosenior] and told him 'I want to leave'. I've seen Cucurella have a meeting with him. But I think Enzo has gone in and said 'I want to leave'.
"One thing you have to do as a manager is never chop your nose off to spite your face. Let the fans look after that situation. Not you. The fans will let you know if they are unhappy with Enzo. But play him on the pitch.
"He is one of Chelsea's best players. It's disappointing as a Chelsea fan, and it's only good news for Man City."
What is Fernandez's contract situation? Could Real sign him?
The Chelsea vice-captain has a contract until 2032, and the Blues would only consider an offer of more than £100m for one of their key players.
Fernandez is not regarded as untouchable by Chelsea, who are planning to sign a new midfielder this summer.
Asked whether the 25-year-old is happy at Chelsea, Rosenior replied: "I can't speak for him.
"What I do know is that when he's been on the pitch, even in the loss at Everton, there was no lack of commitment in his performance.
"In terms of speaking for him and what he wants in his future, that's not for me to speak about."
Real Madrid are planning on signing a midfielder this summer, and players such as Fernandez and Manchester City's Rodri are amongst their targets.
It remains to be seen whether they would ever spend more than £100m on Fernandez when cheaper options will be available.
Chelsea signed Fernandez from Benfica for a then-British record £106.8m three years ago.
He was close to former Chelsea head coach Enzo Maresca, who left the club in controversial circumstances at the start of this year.
Fernandez agent calls decision "completely unfair"
Fernandez's agent Javier Pastore has called the decision "completely unfair" in an interview with The Athletic.
Pastore said: "Enzo didn't understand the situation. When the coach told him, he accepted it because he's a highly professional guy who's always fully committed wherever he is and respects decisions.
"But we don't understand the punishment because he doesn't mention any club or say he wants to leave Chelsea, far from it. He only mentions Madrid, the city, because he was asked which European city he'd like to live in one day.
"He said Madrid because of the language, because it's similar to Buenos Aires and because it's logical - it's only natural for an Argentine to say that - and also because of the culture and the weather.
"But at no point does he say he wants to leave Chelsea or London."
Pastore also revealed talks over a new contract have stalled, adding: "There have been talks about renewing his contract, yes. We started discussing it around December or January, but we couldn't reach an agreement.
"As Enzo's contract still has six years to run, we decided not to renew it because the terms weren't right for us or for the player. Given what Enzo is capable of today, he deserves much more than he's currently earning.
"We haven't reached an agreement and it may be that this annoyed the club, given that he is a hugely important player, but these are things that have to be managed.
"We felt that rather than renewing on terms that wouldn't make the player happy, it was better to leave things as they are and focus on playing and performing well… We don't want to get into discussions about figures, contracts and negotiations when the timing wasn't right.
"Our plan after the World Cup is to meet with Chelsea again and, if there is no agreement, to explore other options."
Rosenior: Cucurella shouldn't have gone public with criticism
Fernandez was not the only Chelsea player to publicly speak out over the international break, with Cucurella criticising the club's policy of signing young players.
The defender, who spoke while on Spain duty, also blamed Chelsea's recent struggles on Maresca's departure.
The Italian's replacement, Rosenior, revealed he has spoken to Cucurella over his comments, but he remains available for selection and could even captain the side on Saturday after name-checking the Spaniard among the options who could take the armband against Port Vale.
Rosenior, though, said Cucurella should not have spoken publicly and should have aired his thoughts privately with the club.
"[I had a] fantastic conversation with Marc yesterday. Half an hour in my office," he said.
"The disappointing thing for me, what we're trying to create here in my time, I've only been here for three months.
"I've said to them [the players] from day one, if they've got any issue with how we do things, to come and speak to me, and speak to the sporting directors.
"My disappointment in Marc's interview is where it went to. I think he should have spoken to us first about the things that he's feeling. I want players to feel like they can speak openly and honestly for the benefit of the football club.
"And those conversations we've had with Reece James, that's why Reece has signed a new contract, because he believes in where we're going. And as a football club, we know we need to improve, myself included, and we actually know what we're going to do in the summer to achieve those objectives."
Asked why Cucurella had not spoken to the club first, Rosenior replied: "Everybody knows Marc Cucurella, knows his character. He's a great character, he's passionate, he wants to do well. He did a long interview where he spoke with passion; he spoke his mind.
"Yesterday, when I was in the office with him for half an hour, it was to remind him that you can come and speak to me, you can be honest with me, and you can be honest with the club about what you want. That takes time.
"I've been here for two-and-a-half months, we've played 20 games, so to build those relationships and those connections takes time.
"But Marc is fully committed, he wants to be here, he's made that very, very clear to me, and he actually believes in where we're moving forward."
Players with PL experience to be targeted this summer
Chelsea will be busy in the transfer market this summer, and signings are expected to include established players with proven Premier League experience.
They will sign a centre-back and a midfielder, while a goalkeeper signing cannot be ruled out - although that could be Mike Penders returning from his loan at sister club Strasbourg.
Strasbourg forward Emmanuel Emegha and Sporting Lisbon winger Geovany Quenda have already signed deals to join Chelsea in the summer.
Rosenior admitted on Friday that the club needed to bring in "players with emotional stability" after Cucurella's criticism over a lack of experience in the squad.
Rosenior said: "Bringing players with emotional stability, bringing good characters in, who in difficult moments can understand what it takes to win in those difficult moments.
"We've had great conversations with the ownership and support directors about what we do in the summer. And we've also had conversations with certain players in the group as well, who are really, really happy with the direction that we're going to go in."
Asked how disruptive Fernandez and Cucurella's comments have been, the ex-Hull boss replied: "It's not ideal. I think a lot of this stems from that we had a really, really difficult 10 days. Probably the most difficult 10 days of my career as a player or a coach.
"I'll go back to the first game against PSG. The belief in the group and what we were doing, the performance was top and it all fell apart in 15 minutes and there was a huge emotional dump from that game, which I think fell through to the next three games that we played.
"Why was there such a big emotional dump? Because the players were so motivated and had so much belief that we could do something really special in the Champions League this year.
"I feel like not just the comments from Enzo, but Cucu's interview as well, stems from that.
"It actually stems from a good place where they want to do well; they want the club to succeed. But in those moments, I think we need more emotional stability as a group of players, from me as the head coach, as a football club, so that we don't respond in the way we have done to the setbacks we've had."
