Vargas suffered a non-displaced fracture of the hamate bone in his right hand Saturday when he attempted to catch a line drive in a minor league game.
Initial X-rays showed no broken bones, but a CT scan performed later Saturday revealed the fracture.
The Mets did not announce a timeline Sunday for how long Vargas would be sidelined. Mets manager Mickey Callaway indicated Saturday, however, that the team did not think Vargas would miss the start of the regular season, even if he doesn't pitch again this spring.
Vargas, 35, signed a two-year, $16 million deal with the Mets last month after going 18-11 for the Kansas City Royals last season.