The James Paget University Hospital at Gorleston said it was experiencing unprecedented levels of demand and announced a "major incident" on Monday.
This means that all beds are full and patients are waiting in A&E.
On Sunday 93 ambulances arrived at the hospital when the average number for that day is usually about 50.
Hospital chief executive Christine Allen said: "All beds at the hospital are full and all additional bed space available when extra capacity is needed is now in use.
"It is important that local people are aware of the current situation at the James Paget University Hospital.
"My message to them is: do not attend our A&E department unless your condition is life or limb-threatening."
The hospital has 396 beds and serves an area of about 230,000 people in east Norfolk and north Suffolk.
A Norfolk hospital has told patients to stay away from its accident and emergency (A&E) unit unless suffering "life or limb-threatening" conditions.