The team announced Tuesday that Jennings will be re-evaluated after a three-week immobilization period. Detroit opens the regular season on Oct. 30 against Washington.
Jennings signed a three-year, $24 million contract with the Pistons in the offseason after joining the team in a sign-and-trade deal with the Milwaukee Bucks.
Jennings is the second member of the Detroit backcourt to go down in the preseason, joining Rodney Stuckey, who is out three to four weeks with an injured thumb.
Jennings, 24, averaged 17.5 points and 6.5 assists in 80 games with the Bucks last season.