Health Protection Scotland (HPS) said 53 wards in 21 hospitals were closed to new admissions and 383 patients and 128 staff were affected.
The highly contagious norovirus causes vomiting and diarrhoea, and is common in hospitals and nursing homes.
Ten NHS boards reported the bug, with NHS Lothian reporting the highest number of affected patients and staff.
Hospitals in Lanarkshire, Glasgow and Dumfries and Galloway were also affected. There were no reports of the bug in the Highlands, Orkney or Shetland.
Health Secretary Nicola Sturgeon said: "Norovirus, or the winter vomiting bug, is a common virus and, as the name suggests, circulates every winter.
"Many parts of Scotland are currently experiencing outbreaks but there is no indication that this year is significantly worse than previous years.
"The number of ward closures is currently higher than the same time last year but around the same as the previous winter."
She urged people to prevent the spread of the virus by following good hand hygiene procedures.
Ms Sturgeon said: "The Scottish Government and health boards will continue to monitor norovirus outbreaks closely, taking every step to minimise its impact on both those who use and work in our hospitals."
Norovirus statistics will be published weekly on the HPS website.