Matz, 25, was scheduled to pitch in a minor league game at the Mets' complex in Port St. Lucie, Fla., to start the final week of spring training. The Mets open the season at home on April 3 against the Atlanta Braves.
"There's a little irritation, and he's got to work that out," Mets general manager Sandy Alderson told reporters Sunday. "We don't think it's anything significant, but it bothers him on extension. He won't pitch tomorrow, and we'll see where that takes him over the next four or five days."
Matz, who underwent Tommy John surgery earlier in his career, was reassured by doctors that he has no ligament damage in the elbow.
Matz said he felt tenderness before his last outing on Wednesday when he gave up five runs and eight hits in four innings against the Miami Marlins. He is 1-1 with a 4.26 ERA in four starts this spring.
"I talked to the doctor right away just to see his thoughts," said Matz, who had a bone spur removed from his elbow after a shoulder issue ended his 2016 season. "He just said this stuff can happen when you're coming back from surgery."
Matz was 9-8 with a 3.40 ERA in 22 starts over 132 1/3 innings last season before being shut down in September.