The injury was suffered on Tuesday night during the Yankees' win over the Twins, although Gardner did take batting practice prior to Wednesday's game.
The Yankees have several options to take Gardner's place in the outfield, including Raul Ibanez, Andrew Jones, and Eduardo Nunez. To replace him on the 25-man roster, the Yankees recalled pitcher Cody Eppler, a right-handed reliever.
The 28-year old Gardner has fared well at the plate so far this season, batting .321 and posting a .424 on-base percentage, while also continuing his strong work in the outfield.
The Yankees will face the Twins on Thursday night in the final game of a four-game set.