The team also transferred Johan Santana to the 60-day DL to free up space on the 40-man roster. Santana has been rehabbing in Florida after shoulder surgery last September.
Young was scheduled to start Saturday night against the Los Angeles Dodgers but had trouble warming up before the game. Dillon Gee pitched well in his place, limiting Los Angeles to two runs in 5 1/3 innings in a game New York won 4-2.
Young had an MRI on his shoulder Sunday morning and the team decided to put him on the disabled list, retroactive to May 2, for the second time this season.
His shoulder was "not to the point where he could let it go 100 percent," general manager Sandy Alderson said Saturday night. "Even 90 percent wasn't going to be possible."
Young has been one of the Mets' best pitchers when he has been healthy, going 1-0 with a 1.87 ERA in four starts. But he missed more than two weeks last month with right biceps tendinitis, and reported tightness in his shoulder during a bullpen session earlier this week.
He didn't experience pain during a series of tests prior to his scheduled start Saturday, though, leaving the veteran right-hander baffled as to the problem.
His next turn isn't until Thursday, a scheduled day off for New York.
The Mets selected the contract of left-hander Pat Misch from Triple-A Buffalo to take Young's place. The left-hander allowed one run in two innings with New York in April, and had been 0-2 with a 6.46 ERA in four starts for the Bison.
He was at Citi Field on Sunday and will work from the bullpen.
"He's here to pitch," manager Terry Collins said.
Santana has reportedly been ahead of schedule following surgery last fall to repair a torn anterior capsule in his left shoulder.
He's already throwing long toss from about 150 feet at the team's spring training complex in Port St. Lucie, Fla., and is expected to begin throwing off a mound soon, though the two-time Cy Young winner is not expected back with the team until at least July.