NHS Highland asked people to avoid the site last week, after 50 people fell ill with the sickness bug.
Consultant microbiologist Dr Chin Lim said three wards remained closed to new admissions and visitors but the rest of the hospital was open.
Tests have confirmed the presence of the bug in wards 7C, 2C and 2A.
In a statement, Dr Lim thanked people for their "patience and understanding".
He added: "While I am pleased that we have been able to reopen to visiting we know norovirus is still in the community so would ask that visitors are limited to two per patient and that if you, or anyone you live with, has had symptoms of diarrhoea and vomiting you refrain from coming into the hospital until you are clear for 72 hours."
Restrictions on visitors have been lifted at Raigmore Hospital in Inverness following an outbreak of norovirus.