Mets general manager Sandy Alderson said Mejia underwent Tommy John elbow surgery, which was performed by team doctor David Altchek.
"It was a clean tear. The elbow looked clean, other than the injury," Alderson said. "So from his standpoint it was an excellent result."
Typically, pitchers need between 12 and 18 months of rehabilitation to return to the mound.
Young had surgery to repair the anterior capsule in his right shoulder. Alderson said the surgery revealed some "fraying" in Young's rotator cuff, which the GM called insignificant.
Young, whom the Mets signed to an incentive-laden one-year contract, suffered the same injury that sent Johan Santana to the operating table in September. He also was felled by the same ailment last season. He opted for rehabilitation rather than surgery in that case.
Santana underwent surgery on Sept. 14 for the injury and is only now nearly due to step on a mound for the first time, with an eye toward a July return to the majors.
Alderson said it was "conceivable" that Young, who relies on a mid-to-high-80s fastball to be effective, will be able to return to the big leagues as an effective starter.
"Even if age is an issue, velocity is not for someone like Chris Young," Alderson said.
In a bit of positive injury news, first baseman Ike Davis was in the clubhouse and said he should be ready to come off the disabled list when he's eligible May 26.
Davis (sprained left ankle) was placed on the disabled list after colliding with Wright while trying to catch a popup last Tuesday night against the Colorado Rockies.
"I feel good," said Davis, who got the boot off his ankle two days ago and is now wearing an air cast. "Obviously I'm walking a lot better right now, and hopefully I'll go down to Florida, and hopefully get everything good, get some ABs and get back here the 26th, I think is the first day [eligible to come off]."
Davis, who's hitting .302 with a team-high 25 RBIs, will head down to Port St. Luice, Fla., on Monday night to begin working out at the team's spring training complex.
Ian Begley is a regular contributor to ESPNNewYork.com. Information from ESPNNewYork.com's Mike Mazzeo was used in this report.