"It's big. We were just counting on him being here a month from now," Rojas told reporters. "This happening is tough. ... We pray that he can pitch for us this year."
Rojas said there was no structural damage to the UCL (ulnar collateral ligament).
On Tuesday, Syndergaard left his second rehab start following his recovery from Tommy John surgery after one inning (16 pitches) as a precautionary measure due to soreness in the elbow. He was scheduled to throw at least four innings for Class A St. Lucie.
His velocity, normally in the mid-to-high 90s, was clocked in the mid-80s by the end of his stint Tuesday.
Syndergaard had pitched four scoreless innings in his first outing for St. Lucie, allowing one hit with five strikeouts while throwing 44 pitches.
Mets acting general manager Zack Scott had said Monday that Syndergaard was on track for a mid-June return to the major league rotation.
Syndergaard is one of several Mets on the injured list and one of four pitchers, along with Carlos Carrasco (right hamstring), Taijuan Walker (right side) and Jordan Yamamoto (right shoulder). Carrasco, who was expected to serve as the Mets' No. 2 pitcher in Syndergaard's absence, is on the 60-day IL and is not expected to return until at least July.
Syndergaard, 28, missed the coronavirus-shortened 2020 season after undergoing Tommy John surgery on his pitching elbow that March. The former All-Star pitcher is scheduled to become a free agent after the 2021 season after reaching a one-year, $9.7 million deal for this season.
He threw a career-high 197⅔ innings in 2019 but posted a career-worst 4.28 ERA. The hard-throwing right-hander has a career 3.31 ERA in parts of five seasons, all with the Mets.
The Associated Press contributed to this report.