Four wards were closed to visitors at Arrowe Park Hospital, Wirral, on Monday before the visiting ban was extended on Thursday.
The ban does not affect Wirral Women and Children's Hospitals.
Gaynor Westray, director of nursing and midwifery at the hospital, said the decision was "in the best interests of our patients".
She said: "The safety of our patients is paramount to us and it is never an easy decision to make but this will help us contain the spread of this highly contagious bug."
The hospital has also asked the public to not visit its accident and emergency department if they have symptoms of the bug.
Norovirus - which causes vomiting, stomach cramps, fever and diarrhoea - is easily spread from person to person.
Symptoms usually begin between 12 to 48 hours after a person becomes infected, with most healthy people making a recovery within one to three days.
Arrowe Park has not given an indication of how long the ban is likely to remain in effect.
A hospital has suspended visits to patients on all its wards following an outbreak of the norovirus bug.