The Braves said Medlen suffered the injury to his ulnar collateral ligament. He has been scheduled for an MRI on Thursday.
Medlen left his last start on Friday in Cincinnati after he was hit on the inside of his right forearm by a pitch from Johnny Cueto.
The right-hander showed no sign of discomfort against the Mets before throwing a pitch outside of the plate to Jose Reyes with one out in the fifth. Medlen took a couple of hops off the mound. Manager Bobby Cox and trainer Jim Lovell quickly came out of the dugout to the mound.
"It was just that pitch," Medlen said. "I felt a little tightness in my elbow. It's still pretty tight so we'll see tomorrow. ... Anytime it's your career, anytime anything goes wrong with your arm you're a little worried."
Medlen appeared to try to flex his arm before leaving the game.
"He couldn't throw another pitch so, obviously, something popped in there," said Cox. "That's my opinion. I'm no doctor."
Medlen gave up four hits and two runs in 4 1/3 innings. Left-hander Mike Dunn took over for Medlen.
The second-year right-hander has been one of Atlanta's most effective starters after taking over the No. 5 spot in the rotation. The Braves are 13-1 in Medlen's 14 starts, including 11 straight wins. He is 6-2 with a 3.68 ERA.
Cox said the Braves would immediately make plans for a roster move.
The loss of Medlen would be a blow to the Braves' hopes of holding off Philadelphia in the NL East. He has been one of Atlanta's most effective starters after taking over the No. 5 spot in the rotation from Kenshin Kawakami.
Kawakami has appeared in only one game in relief since his last start on June 26. Cox said Kawakami may not be ready to start if the Braves must replace Medlen.
Information from The Associated Press was used in this report.