The three-time Cy Young Award winner was placed on the 15-day disabled list before the Mets' game against the Florida Marlins on Wednesday night.
Martinez was injured Tuesday night, returned to New York on Wednesday and was examined by Dr. David Altchek at the Hospital for Special Surgery.
"We just have to play and get after it," Mets manager Willie Randolph said after Wednesday night's 13-0 win over the Marlins. "We're going to miss him. I'm not trying to downplay losing Pedro. It's unfortunate. He worked real hard to get back to this point. I know he was looking forward to being in the clubhouse around this team to help us win."
"We're looking forward to those guys stepping up," Randolph said.
Martinez allowed four runs in 3 1/3 innings during a 5-4, 10-inning defeat on Tuesday, limping off the mound after injuring himself during a pitch.
"Everyone feels bad about that," Perez said. "We just have to be prepared and continue to play."
The Mets filled Martinez's roster spot by purchasing the contract of pitcher Nelson Figueroa from Triple-A New Orleans.
They could put Figueroa in the rotation to start against Philadelphia at home next week. Jorge Sosa is a long shot possibility for the rotation.
"You can't feel sorry for yourself," Mets third baseman David Wright said. "When somebody goes down in the lineup the hitters rally around one another and pick up the slack. I expect the same from the pitchers."