This is the first time in his 15-year major league career Green has gone on the DL.
The injury occurred Friday when he fouled a ball off his foot. He continued to play before undergoing tests after the game.
Green, who is batting .314 with five homers and 22 RBI, is expected to start running in 10 days.
To replace Green on the roster, the Mets recalled outfielder Ben Johnson. Johnson was hitting .282 with two home runs and 11 RBI in 21 games with Class AAA New Orleans.