Smith is nursing lingering knee, ankle and thumb injuries, a team spokesman said in an email.
The 30-year-old Columbus native was 20-of-45 passing for 231 yards last weekend against Edmonton and has completed just 47.7 per cent of his passes this year.
The former Heisman Trophy winner has struggled this season for the Alouettes, who took a 1-5 record into Saturday night's game at 4-2 Saskatchewan.
Backup Alex Brink was expected to replace Smith under centre. Entering play against the Roughriders, the Alouettes were averaging a league-low 16.3 points per game.