WASHINGTON—A General Motors Co. employee warned in 2005 that the auto maker had a “serious safety problem” with the design of ignition switches used on the 2006 Impala that could lead to a “big recall,” but the company didn’t recall the vehicles until early this week.

The employee, Laura J. Andres, told other GM engineers that the 2006 Chevrolet Impala she was driving in August 2005 shut off after she went over a bump in a road, and in a later Aug. 30, 2005 email warned that the problem appeared to be…