Chelsea could have been handed an all-English last-16 tie against Newcastle, but Eddie Howe's side will face Spanish champions Barcelona.
Premier League leaders Arsenal, who topped the Champions League table with a perfect record, face German side Bayer Leverkusen.
Six-time winners Liverpool take on Galatasaray, while Tottenham have been handed a tie against Atletico Madrid.
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This is the fifth consecutive season Man City and 15-time winners Real Madrid have been drawn in the Champions League knockouts.
Round of 16 schedule confirmed
First legs: Tuesday March 10 (kick-off 8pm unless stated)
Galatasaray vs Liverpool, kick-off 5.45pmAtalanta vs Bayern MunichAtletico Madrid vs TottenhamNewcastle vs Barcelona
First legs: Wednesday March 11 (kick-off 8pm unless stated)
Bayer Leverkusen vs Arsenal, kick-off 5.45pmBodo/Glimt vs SportingPSG vs ChelseaReal Madrid vs Man City
Second legs: Tuesday March 17 (kick-off 8pm unless stated)
Sporting vs Bodo/Glimt, kick-off, 5.45pmArsenal vs Bayer LeverkusenChelsea vs PSGMan City vs Real Madrid
Second legs: Wednesday March 18 (kick-off 8pm unless stated)
Barcelona vs Newcastle, kick-off 5.45pmBayern Munich vs AtalantaLiverpool vs GalatasarayTottenham vs Atletico Madrid
Route to final revealed with Arsenal supercomputer's favourites
Man City, Liverpool and Chelsea have been placed in what appears to be the hardest side of the draw.
Were City to progress past Real Madrid, they will face either Bayern Munich or Atalanta in the quarter-finals, while Chelsea and Liverpool will meet in the last eight if they knock out PSG and Galatasaray respectively.
Meanwhile, Arsenal will play either Bodo/Glimt or Sporting if they beat Leverkusen. Were they to reach the semi-finals, Arsenal's opponents will be Newcastle, Barcelona, Atletico or Tottenham.
Analysis: A favourable draw for Arsenal?
A trip to Germany awaits for Arsenal as they face Bayer Leverkusen for the first time since a 4-1 win in 2002. Win that tie, and it's Bodo Glimt or Sporting next. It's a favourable draw, especially given the alternative was a potential quarter-final against Manchester City.
It's only two years since Leverkusen won the Bundesliga under Xabi Alonso but they are no longer the same team. Having finished second last season, they now sit sixth, with Kaspur Hjulmand at the helm after Erik ten Hag's brief spell in charge ended in September.
"We are very excited to play the next round," said Mikel Arteta at his press conference on Friday. "We have earned the right to be in a strong position with what we've done in the group stage, and that's it.
"Now we need to start to analyse them and find ways to be better them and try to go through the tie."
Analysis: A tough run of games for City
Not only will Manchester City have two tough assignments against Real Madrid coming up, but the two ties against Madrid will be in the middle of what looks a daunting run of fixtures for Pep Guardiola's side.
Between March 7 and March 22, City will have to play away to Newcastle in the FA Cup, then travel to Madrid in midweek, before returning to Premier League action at West Ham.
They will then face Real Madrid in midweek before taking on Arsenal in the Carabao Cup final on Sunday March 22.
Analysis: What lies ahead for Liverpool?
Liverpool's last meeting with Galatasaray, the 1-0 loss in the league phase in September, occurred at the beginning of the dismal run of results that threw their season into disarray. Arne Slot has them in better shape ahead of their next meeting.
The Reds have avoided a last 16 tie against Atletico Madrid but their route to the final, beyond the meeting with Galatasaray, for which they will be strong favourites, looks daunting, with Paris Saint-Germain, Chelsea, Manchester City, Real Madrid and Bayern Munich potentially standing in their way.
Before that, though, it's a potentially awkward trip to Turkey, and a reminder that any side containing Victor Osimhen has to be taken seriously.
Analysis: Brutal March schedule for Newcastle
The Champions League draw has handed Eddie Howe's Newcastle a tough run of fixtures in March.
The Magpies will play Man Utd, Man City, Barcelona, Chelsea, Barcelona again and then arch rivals Sunderland back-to-back.
The games - including a FA cup tie with Man City - will form a defining period in Newcastle's season. As shown in the graphic above, Eddie Howe's side could play a maximum of 66 fixtures this season - the highest total for any Premier League club.
Analysis: Chelsea facing tough route to CL final
Chelsea have been placed in what appears on paper at least to be the hardest side of the Champions League draw.
Were they to progress past holders PSG, Chelsea will face either Galatasaray or Liverpool in the quarter-finals.
And if they reach the last four, Chelsea's opponents will be one of Real Madrid, Man City, Atalanta or Bayern Munich.
Analysis: How will Spurs juggle CL?
Head coach Igor Tudor said it was "not ideal" for Tottenham to be in the Champions League while also fighting a Premier League relegation battle - and Friday's draw highlights the balancing act he has.
Tottenham will go away to Atletico Madrid in the first leg of their last-16 tie and then play Liverpool in the Premier League before hosting the Spanish side for the second leg.
But crucially, that second leg - when a Champions League quarter-final place could be on the line - comes just days before a huge relegation six-pointer at home to Nottingham Forest.
How will Tudor manage the battle on two fronts, given how he flagged the physical and mental demands the Champions League will place on his already injury-hit squad?
Home advantage in second legs for seeded teams
The top eight teams from the league phase are seeded and will have home advantage in the second leg of their round of 16 games.
This will extend to the quarter-finals for the teams that finished in the top four of the league phase - Arsenal, Bayern, Liverpool and Spurs - if they progress.
For Arsenal and Bayern, the top two, they will also have home advantage in the second leg of their semi-final if successful.
Any team that eliminates a seeded team will take their privileges.
When will QF and SF fixtures be announced?
The quarter-final match schedule will be confirmed on March 19, while the semi-final schedule will be communicated on April 16.
When are the 2025/26 Champions League knockout stages?
Round of 16: March 10-11 and 17-18Quarter-finals: April 7-8 and 14-15Semi-finals: April 28-29 and May 5-6Final: Saturday May 30
Where is the Champions League final?
The 2025/26 Champions League final will take place in Budapest at the Puskas Arena on Saturday May 30.