Seventy-five people have been airlifted from the Buchan Alpha installation in the North Sea after warnings of high waves.
Talisman Sinopec Energy UK said that the shutdown began on Thursday and normal operations will resume when the weather improves.
Forecasters have warned that gusts of up to 80mph could hit parts of Scotland from Sunday into Monday, particularly the Northern and Western Isles.
The Met Office has issued yellow "be aware" severe weather warnings of high winds for Orkney, Shetland, the Highlands, Western Isles and Strathclyde.
It said: "Gale or severe gale force winds are expected from Sunday afternoon through into Monday morning, particularly for the Western and Northern Isles, with the potential for gusts in excess of 70 or even 80 mph at times."
It has also issued yellow warnings of ice for all parts of Scotland and snow for Strathclyde, Central, Tayside and Fife.
Talisman Sinopec Energy UK said: "Talisman Sinopec Energy UK can confirm that it has today safely completed a planned downman of 75 personnel from its Buchan Alpha installation as a result of severe weather forecasts.
"As per the installation's Safety Case, we began the planned procedure on Thursday (23 January) as a result of severe weather forecasts and in advance of the sea state exceeding the stated level over the weekend.
"Production was shutdown on Thursday and will remain shut down while we continue to monitor the weather conditions. We will upman, and normal operations will resume when conditions improve.
"The safety of all of those who work on our sites remains of paramount importance.
"The Health and Safety Executive have been informed."
The weather affected road travel today, with the snow gates closed at Glenshee and Cairn O'Mount.
Police Scotland said that there were a few minor collisions on the A9 earlier where there was a lot of surface water.
The Skye Bridge was closed to high-sided vehicles for a time due to high winds