The pipe handles 40 percent of the daily outflow from the firm's North Sea oil drilling, The Scotsman reported Wednesday.
The unexploded World War II-era mine close to the Forties pipeline is 13-feet long, the newspaper said.
BP has spelled out options, which include leaving the mine where it is or moving it for detonation elsewhere. The second option, however, would mean shutting down the pipeline temporarily, the firm said. That would halt delivery of about 500,000 barrels per day.
The 105-mile pipeline serves both British and Norwegian oil production from the North Sea.
"An unidentified object was observed lying next to the BP-operated Forties pipeline in the North Sea. The object was subsequently identified by specialists as a piece of Second World War military ordnance. It is lying adjacent to the pipeline approximately 40 kilometres [24.8 miles] off the coast from Peterhead," a company spokesman said.
He said the mine, found March 22 during a routine inspection, was not an immediate threat.
"A lot of operators feed into that pipeline, so there could be a significant knock-on effect from a shutdown," RMT union organizer Jake Molloy said.
"It could cause a number of operators a real headache."