Hinch aggravated the injury on two swings in Tuesday night's game against Oakland. On a wet field at Comerica Park, he slipped while hitting a foul ball.
Hinch is batting just .188 with a home run and seven RBI in 21 games. He was sidelined with the same injury from July 18-Aug. 2.
To fill his roster spot, the Tigers recalled catcher Brandon Inge from Triple-A Toledo of the International League.
In his first stint with the Tigers this year, Inge batted .150 with four homers in 56 games. He was optioned to Toledo on June 18.
At Toledo, Inge was batting .275 with nine doubles, five home runs, and 15 RBI in 39 games.
""They sent me down here to get my offense on line and I feel that I have for the most part," Inge said. "It was a matter of keeping the right attitude."