The recall covers the CC from the 2009 through 2016 model years, as well as the Passat sedan and wagon from 2006 through 2010. All have four-cylinder gasoline engines.
VW says in government documents that the fuel pump control computer can lose electrical power. That can stop gas from flowing and cause the engine to stop. That problem also can make the fuel pump continue running after the car is shut off.
VW will notify owners about the problem in October and send a second letter when replacement computers are available.
VW says it has no reports of crashes or injuries in the U.S. caused by the problem.