Smith suffered the injury during Wednesday's 115-92 loss to the Milwaukee Bucks.
The 30-year-old has been one of Detroit's top bench contributors this season, averaging 9.2 points, 3.0 assists and 1.9 rebounds in 24.4 minutes per game as the primary backup to starter Reggie Jackson.
He is also in the final year of the three-year, $18 million contract he signed with the Pistons in 2016.
Smith has been a highly durable player during his stint in Detroit, as he appeared in 81 games in 2016-17 and played all 82 games last season.
The North Carolina native has suited up for 10 different teams during his nine-year NBA career, and it wasn't until 2015-16 when he truly hit his stride with the New Orleans Pelicans and Philadelphia 76ers. That season, the Wake Forest product averaged a career-high 12.6 points, 6.5 assists and 4.0 rebounds per game.
With the Pistons, Smith has averaged 10.0 points, 4.6 assists and 2.7 rebounds per contest in 185 games.
Until Smith is able to return for the 13-9 Pistons, look for Langston Galloway to play an even bigger role in the backcourt rotation and expect veteran point guard Jose Calderon to see more minutes as well.