According to the Pittsburgh Post-Gazette, Leftwich will likely end up on season-ending injured reserve.
Leftwich was slated to be the Steelers' No. 2 quarterback behind starter Ben Roethlisberger this season.
The injury occurred early in the third quarter on a six-yard scramble. It was Leftwich's first series of the night.
Batch and Dixon combined to lead Pittsburgh to a 3-1 record last season while Roethlisberger was suspended for the first four games.
Information from The Associated Press contributed to this report.