The company wants to verify if steering shafts were installed properly on the vehicles. Most of them will also be checked for a potential transmission problem.
The cars were manufactured in Lordstown, Ohio and sold in the U.S. and Canada.
GM says no crashes or injuries have been attributed to either issue and the National Highway Traffic Safety Administration has received no consumer complaints.
More than 25,000 Cruzes were sold just last month.
The Associated Press contributed to this story.