The recall affects 5- and 6-Series BMWs built between 2003 and 2010, BMW said in a statement.
In some remote cases, the battery cable cover inside the boot of these vehicles may be incorrectly mounted, it said.
This can result in the electrical system malfunctioning, the vehicle failing to start and, in some cases, to charring or fire, the company said, adding it was not aware of any accidents or injuries to people due to the problem.
Fewer than 1 percent of the cars BMW has so far inspected for the issue have exhibited the problem, a BMW spokesman said. So far, the spokesman said, there have been no reports of fires.
BMW said it was writing to car owners. The repair procedure in a BMW partner workshop would take about 30 minutes to an hour and would be free of charge to customers, it added.
The recall affects about 368,000 cars in the United States and about 293,000 cars in Germany, BMW said. Another 109,000 cars are subject to the recall in Britain and about 102,000 in China, BMW said.
In some European countries, the trunk is called the car's boot.
(Reporting by Jan Schwartz and Jonathan Gould in Frankfurt and Bernie Woodall in Detroit; Editing by David Hulmes, Gerald E. McCormick and Steve Orlofsky)