The fields affected, and another eight associated platforms, produce about 10% of the UK's oil output.
Hydrocarbons were detected inside a leg of the Cormorant Alpha platform.
Its operator, Taqa Bratani, has removed non-essential workers as a precaution and said the leak had been contained.
Shutting down the platform affects the whole Brent pipeline system.
The oil leak at Cormorant Alpha was discovered on Monday and non-essential crew were taken off the installation by helicopter.
Taqa, also known as Abu Dhabi National Energy, said nothing had leaked into the sea and a technical team was investigating the source.
Taqa said on Wednesday afternoon that it was "currently evaluating plans to restore the throughput of an estimated 80,000 barrels per day in the Brent pipeline, excluding any Cormorant Alpha production."
A spokesperson said: "This action would occur after thorough technical assurance has established that it can be undertaken safely and without any increased risk."
The BBC understands the rest of the Brent pipeline system can no longer operate because Cormorant Alpha, which is situated some 94 miles from Lerwick in Shetland, is a crucial pumping station.
Eight other platforms have shut down with up to 27 North Sea fields affected.
The Dunlin, Thistle, Northern Producer, Murchison, North Alwyn, Tern, Eider and North Cormorant platforms are also affected.
Oil and Gas UK - the offshore industry body - said oil transported through the Brent pipeline system represented 10% of the UK's North Sea oil production.
The amount of output affected is 90,000 barrels per day.
It is not yet known what potential impact the shut down could have on petrol station prices.
However Prof Alex Kemp, an oil economist at the University of Aberdeen, said the closure would have a limited impact on oil prices.
He told BBC Radio Scotland's Good Morning Scotland programme: "What we have is an incident which impacts on the Brent pricing system which is used as a marker price for a lot of the world's production.
"If it continues one would expect a limited affect on the Brent price.
"But the Brent price doesn't just depend on Brent production, it depends on production from a lot of other fields.
"The effect should be limited because although the Brent price is the marker for a huge volume of oil in the world market, Brent production constitutes not all that big a proportion of the total."
Enterprise Minister Fergus Ewing said: "The Scottish government, including Marine Scotland, are monitoring this situation closely.
"No release of hydrocarbons has been reported and all non-essential staff on the platform have been safely removed.
"The Health and Safety Executive are investigating and will determine when the pipeline system can be opened again subject to any relevant safety measures being put in place."
He said the loss "does not impact security of supply at this time".
A pipeline system servicing up to 27 oil fields has been shut down after a leak on the Cormorant Alpha platform, north-east of Shetland.