The recall affects Buick LaCrosse full-size cars and Cadillac SRX crossover SUVs from the 2013 model year.
The company says a software problem can cause transmissions to unexpectedly shift into sport mode. That can override any slowing effect from the transmission, increasing the risk of a crash.
GM says no crashes or injuries have been reported.
GM will reprogram the transmission at no cost to the owners. The recall is expected to start March 28.
The Buicks were built from April 25, 2012 through March 6, 2013. The Cadillacs were built from May 29, 2012 through Feb. 18, 2013.
Most of the cars and SUVs, about 27,000, were sold in the U.S., with another 1,300 sold in Canada. The rest were sold in Mexico and exported to other parts of the world, GM said.