Ward 2A is the latest to close at Raigmore Hospital, Inverness after wards 2C, 6C and 7A earlier this week.
NHS Highland has suspended visiting to each of the closed wards and imposed a restriction on visiting to all other wards in the hospital.
It said it is seeking support from the public to help prevent it spreading to other wards.
Vanda Plecko, consultant microbiologist at NHS Highland, said: “We can confirm that a number of patients have tested positive for norovirus.
“We have placed a suspension on visiting in wards 2C, 6C, 7A and 2A for the time being.
“In the wards not affected we ask that visiting is restricted to two visitors per patient and would once again request that children do not visit the hospital.
“We would ask that anyone coming into the hospital needs to be clear of any norovirus symptoms for at least 48 hours. By doing this we will limit the spread as much as possible.
“For the four wards affected (wards 2C, 6C, 7A and 2A) we would ask that all non-essential visitors stay away from the hospital.”
Those who feel visiting is “essential” should contact the ward first by phone before coming to the hospital.
Patients can also keep in touch with loved ones using the Hospedia system.