There were 159 personnel on the Cormorant Alpha platform when the leak was discovered on Monday. Ninety-two non-essential staff were evacuated from the platform, which is 94 miles off Shetland and forms part of the Brent field.
The 80,000 barrels-a-day Brent pipeline system, which makes up more than 10% of all UK offshore production, was shut after the problem was detected in a leg of the platform, raising fears of a surge in oil prices.
Taqa Bratani, which replaced Shell as operator of Cormorant Alpha platform, said the process of restarting the Brent pipeline had begun after investigations found no connection between the Brent system and the pipeline involved in the leak.
"The process of restarting Brent throughput follows a thorough technical evaluation that shows it is safe to do so without any increased risk to Cormorant Alpha," Taqa said. It earlier said none of the oil had been released into the environment and investigations were continuing to discover the source of the leak.
Shell said the shutdown has not had any direct impact on its Brent Field installations and offered to help Taqa with the repairs.