The warning came after 92 workers were safely evacuated from the Cormorant Alpha platform, 94 miles off Shetland, which is part of the Brent field making up more than 10% of all UK offshore production.
It was sparked by the discovery of hydrocarbons in one of its legs.
Oil traders said the shutdown of the Brent pipeline system means it is facing losses of more than £40 million which could be passed on to consumers in the form of higher prices.
Benno Spencer, the managing editor of EMEA crude for commodity pricing specialist Platt's, said: "This is obviously likely to have a marked impact.
"The big question on everyone's minds is how long it will be out for, but traders suspect it will be at least seven days.
"If so, that's about 15% of the total monthly production for the Brent-Ninian stream, which is semi-alarming."
The rig's operator Taqa Bratani left 67 essential staff on board, but stressed there was no environmental risk and that the decision to move workers onshore was merely a precaution.
It flew out three specialists to assess the seriousness of the problem. It would not comment on the likely duration of the closure, saying it would make another statement today.
Cormorant Alpha channels oil production from 20 oil fields, running the Brent pipeline to the Sullom Voe terminal in the Shetlands.
Yesterday the entire 150km pipeline plus eight other feeder platforms had all closed, including Dunlin, Thistle, Northern producer, Murchison, North Alwyn, Tern, Eider and North Cormorant.
The remaining fields are understood to have continued producing crude but will have to use tankers to store it, raising the prospect of expensive outlays.
The UK Treasury will be braced for the impact on tax receipts from one of its most valuable contributors, while any hit to oil companies is liable to be passed on to refineries and eventually consumers.
Cormorant handles 90,000 barrels per day of crude out of a North Sea average of 850,000.
Brent crude is the benchmark against which two-thirds of the world's oil supplies are priced, meaning UK production has disproportionate importance even though it is a relatively small chunk of total worldwide daily production.
The stream is one of four of the blends that go towards the basket that determines the price, along with Forties, Ekofisk and Oseberg.
"So far what we have seen today is that Total bid for a cargo of Brent to a level that surpassed the previous level for the Brent-Ninian blend," said Mr Spencer. "That perhaps indicates a price rise because of the platform and what's going on with improving refining margins."
Chris Cook, a former director of the International Petroleum Exchange, agreed the seriousness depended on the duration of the closure.
He said: "90,000 barrels per day is stripping out four cargoes of crude per month.
"That is material. It's because a tiny amount of oil actually prices the whole global oil market."
Yesterday Brent fell more than 1% to $110.39 (£68.57) a barrel, having risen sharply the day before.
Taqa Bratani, which is Abu Dhabi's national energy company, replaced Shell as the operator of Cormorant Alpha after buying out Shell's interests in 2009. It is responsible for 42,600 barrels per day from the Brent system, which is jointly owned by 21 companies.
The leak announcement came only hours after Taqa had announced that it had set a North Sea record by delivering oil from its Cormorant East field only 85 days after it was discovered. Taqa holds a 60% stake in the field, one of whose junior partners is Dana Petroleum.
A Taqa spokesman said: "The situation is completely stable at Cormorant Alpha. There is no danger to remaining personnel on the platform or to the platform and absolutely no danger to the environment.
"An investigation is under way. We just have to wait for the results."