An MRI disclosed the extent of the injury after the Reds originally said it appeared to be a strained hamstring. Griffey was hurt in the collision with Chicago Cubs catcher Joe Girardi in the seventh inning of Monday night's game.
Griffey could be available for the Giants series next week in San Francisco, depending on how well he progresses in rehabilitating the leg, Reds spokesman Rob Butcher said.
The Cincinnati outfielder had walked and was trying to score from first on a double to left field by Dmitri Young. The relay by shortstop Ricky Gutierrez got to the plate well ahead of Griffey, who crashed into Girardi, and was tagged out.
Griffey lay on the ground several minutes before limping to the clubhouse.
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