Reynolds has yet to play in a major league game, but he did appear on the NLDS and NLCS rosters last year after Ruben Tejada suffered a fractured right leg during Game 2 of the opening round.
The Mets had been playing down a bench player since Wilmer Flores went on the disabled list last week with a mild hamstring strain. Sean Gilmartin was promoted at that point to cover the bullpen, with Matz active but unavailable.
Reynolds, 25, was hitting .238 with two homers and 10 RBIs in 130 at-bats with Las Vegas. He has started games at second base, third base and shortstop this season.
Reynolds was selected over Ty Kelly and T.J. Rivera in part because he already is on the 40-man roster.