Matz will not need to go on the disabled list, Callaway said. The strain is near the knuckle of the finger.
The team does not know if Matz will make his next scheduled start. He left his start against the Atlanta Braves after three innings on Tuesday night with the injury.
Matz was hurt during a fourth-inning at-bat Tuesday night in which he doubled. The bat flew out of the pitcher's left hand and bent back the middle finger in the process. The injury prevented Matz from pitching in the bottom the inning.
The Mets are recalling relievers Tim Peterson and Buddy Baumann from Triple-A Las Vegas and right-hander Scott Copeland from Double-A Binghamton to reinforce their beleaguered bullpen, which has surrendered late leads in three of their past four games, including Tuesday night's 7-6 loss to the Braves.
Information from The Associated Press was used in this report.