The injury occurred in the bottom of the first inning when the 26-year-old rookie right-hander was stuck by a bouncer off the bat of the Mets' Endy Chavez.
Rasner attempted to stay in the game, throwing several pitches under the supervision of Yankees trainer Gene Monahan, Manager Joe Torre, and pitching coach Ron Guidry, but eventually left the field in obvious pain.
Rasner is the sixth rookie pitcher used by the Yankees' beleaguered staff this season, and the 10th starter in all.
The Yankees plan to start right-hander Tyler Clippard in the finale of the three-game series at Shea Stadium Sunday night.
Clippard will make his Major League debut.