The company, known also as Taqa, said it confirmed a leak from the platform and has since shut it down along with eight other installations in the North Sea.
"The hydrocarbons are contained within the platform leg and none have been released into the environment," the company said in a statement.
The installation is located about 232 miles off the coast of Scotland. The company said it deployed helicopters to pull non-essential crew members from the installation. Taqa stated that all 159 workers on site were safe.
"We have stopped all non-essential work on the platform to focus all our efforts on addressing this issue," the company said in a statement.
The Cormorant Alpha platform processes about 90,000 barrels of crude oil per day.
A 2011 release of 1,300 barrels of oil from Shell's Gannet platform in the North Sea was the largest oil spill in the region in more than a decade.
No oil from the Gannet spill reached shore and much of the original sheen dispersed naturally.