Wong, 25, is batting .222. He signed a five-year, $25-million contract extension this spring but has been the odd man out much of this season. Matt Carpenter is moving to second base and Peralta will be the primary third baseman, making room for Cuban rookie shortstop Aledmys Diaz.
Wong was a first-round draft pick in 2011. He batted .262 with 11 homers and 61 runs batted in last season.
Peralta had surgery in March for ligament damage to his left thumb.
New York Mets outfielder Juan Lagares has a partially torn ligament in his left thumb.
John Ricco, Mets assistant general manager, said Lagares will need surgery at some point.