Tatis was hurt when he attempted to make a diving catch on pitcher Odalis Perez's double. Tatis landed on his shoulder and stayed on the ground as the ball rolled past him for a double. He was replaced by Nick Evans.
New York manager Jerry Manuel said Tatis would not return during the regular season or for a possible playoff run.
"He's done," Manuel said after his team's 1-0 loss. "That's very discouraging, to lose a big piece of where we are and what we've accomplished so far."
Losing Tatis hurts the Mets, who fell out of first place in the NL East, a half-game behind Philadelphia. New York also is missing second baseman Damion Easley (quadriceps), another productive right-handed bat.
"When we lose Tatis, we definitely have to reassess where we are offensively," Manuel said.