Total has confirmed 11 staff on the Gryphon floating production and storage vessel have tested positive for the virus.
The company said the platform has been reduced to essential personnel only and a deep clean is being carried out.
A spokesman for Total said: “We have detected positive results in 11 people using our offshore point of care test machines and all are being down-manned for medical assessment and isolation onshore.
“As a precautionary measure, we have also decided to retest everyone on the facility, perform a deep clean and reduce the number of people on board to essential personnel only.
“Total tests everyone for Covid-19 before they are allowed fly to work offshore.
“Whilst no system can be 100% effective, our stringent approach to testing has so far successfully minimised the number of cases of Covid-19 at our work sites during the pandemic.”