Three people have been quarantined in a bid to prevent the spread of the winter vomiting bug.
The outbreak comes amid fears of a surge of the virus after Chief Medical Officer Sir Harry Burns declared the "season" had begun on October 29, five weeks earlier than last year.
He said: "This may be indicative of a higher than normal level of norovirus circulating this winter."
Latest figures show 16 hospitals across the country had 24 wards closed due to outbreaks, with 208 patients suffering from the sickness and diarrhoea bug.
The rig, the EnQuest-owned Heather installation, reduced staff numbers after workers began complaining of feeling unwell.
The platform, 145km north- east of Shetland, is staffed by Petrofac employees.
A Petrofac statement said: "We can confirm there are currently three suspected cases of norovirus on the installation.
"Personnel who have contracted the virus have all been provided with medical support as required and quarantined in designated cabins.
"All reasonable steps have been taken to contain the spread of the virus, and support and guidance is being provided by onshore doctors and occupational health professionals including NHS Grampian's Health Protection Team. As an additional precautionary measure we are reducing the number of non-essential personnel on the installation to limit further spread of the virus."
The norovirus bug is usually spread through contaminated food or water or by contact with an infected person, surfaces and objects.
It can be passed on in work environments if those suffering from it do not wash their hands.
As well as sickness and diarrhoea, people will generally have flu-like symptoms, such as headaches, and a fever.
Sufferers are advised to stay away from GP surgeries during an infection due to the risk of passing on the virus, so there is no clear way of measuring how many cases have been detected. However, experts estimate there are around 290 cases of norovirus in the community for every single case which is reported.
Cases are known to increase during winter, with oil workers particularly at risk due to living and working in close quarters.
A Health and Safety Executive (HSE) spokesman confirmed Petrofac had been in contact about the outbreak. He said: "HSE has been made aware of the situation. We are continuing to monitor the situation."