Right-handed reliever Jeff Brigham was recalled from Triple-A Syracuse.
Carrasco joins right-hander Justin Verlander (upper back) and left-hander José Quintana (ribs) among Mets starters on the IL. Tylor Megill and David Peterson have been filling in since the start of the season, and José Butto was called up from the minors to make a spot start Sunday in Oakland.
Verlander is expected to throw live batting practice Sunday and could make a rehab start as soon as April 28, according to manager Buck Showalter. Verlander threw a bullpen on Tuesday.
Carrasco felt soreness during a side session between starts this week. An examination confirmed swelling in his elbow and he was sent back to New York. He was put on the IL retroactive to April 16.
"We're waiting to hear results of what's going on there structurally," Showalter said. "We don't know yet."
The 36-year-old Carrasco is 0-2 with an 8.56 ERA in three outings.
New York will need to fill Carrasco's spot in the rotation Friday at San Francisco, but Showalter did not say who would start. The Mets have right-hander Max Scherzer scheduled to pitch Wednesday against the Los Angeles Dodgers.
Also on Tuesday, right-hander Dennis Santana was sent outright to Syracuse with reliever Tommy Hunter close to a return from a back injury. Hunter could be activated Wednesday.
"We'll just see where we are when the smoke clears tonight," Showalter said. "The problem is that we can't get anybody here tomorrow, so that's why Tommy is here now."