Portsmouth's NHS Trust has declared a 'critical incident' because of what it's called "extreme pressures" on its services.
The Queen Alexandra Hospital says it has limited space to treat people with life threatening conditions and injuries.
It's asking people not to attend unless it's an emergency.
In a statement, the trust said:
"Our beds are full and our Emergency Department remains full with patients requiring admission.
"We have limited space to treat emergency patients and we are only able to treat patients with life threatening conditions and injuries.
"Please do not attend the ED unless it's an emergency."
They added non-emergency attendances will not be seen and will instead be redirected to the Urgent Treatment Centres at St Mary's Hospital, Gosport and Petersfield.
It comes hours after the South Central Ambulance Service (SCAS)declared a "critical incident" due to "extreme pressures" it's facing on its services.
SCAS, which operates across Berkshire, Buckinghamshire, Oxfordshire and Hampshire, said its staff are continuing to "work extremely hard" to manage the situation.