A total of 30 patients have experienced sickness and diarrhoea and nine staff have also reported the symptoms.
Ward 12, for stroke patients, is the third ward to be shut to admissions and transfers and to be subject to visitor restrictions since Monday.
General medical wards nine and 10 are also closed to new patients.
Dr Martin Connor, consultant microbiologist and infection control doctor, said: "We appreciate that this temporary visiting restriction to wards nine, 10 and 12 may cause some frustration, but this measure will allow us to help prevent further spread of the infection and ensure safe patient care and dignity, at this difficult time.
"Where circumstances are such that relatives are concerned about the need to visit their loved ones in wards nine, 10 and 12, they are asked to contact the ward before coming to the hospital.
"All members of the public who plan to visit other areas of the hospital are asked not to visit if they are suffering symptoms of nausea, vomiting or diarrhoea, and to comply with the hand hygiene and infection control measures in place."
Three wards at Dumfries and Galloway Royal Infirmary will be closed over the Easter weekend following an outbreak of norovirus, the NHS has confirmed.