Harvey will be prescribed rest for now and treatment plans will be determined later.
Harvey had already thrown 178 1/3 innings this season and gave up two runs on a career-high 13 hits over 6 2/3 innings in his last start, a loss to the Detroit Tigers on Saturday. He said he felt tired after the game and reported having right forearm pain.
"It's not good news, obviously ... Over the next 2 or 3 weeks ... the ultimate treatment will be determined," Mets general manager Sandy Alderson said. "This is not a career-ending injury under any stretch of the imagination. We're fortunate we have a lot of pitching depth in our organization."
Alderson said that Harvey had been getting preventative elbow treatment since spring training, and is not sure when Harvey's forearm trouble began.
That treatment could mean Tommy John surgery, which would end Harvey's 2014 season.
Harvey, 24, was the National League's starting pitcher for All-Star Game at Citi Field in July and is 9-5 with a 2.27 ERA and 191 strikeouts, his first full season with the team.