Stauffer, 33, was selected over Dillon Gee because Stauffer has experience out of the bullpen.
Stauffer has pitched parts of 10 seasons in the majors, including going 1-0 with a 6.60 ERA with the Minnesota Twins this season.
He was signed by the Mets to a minor league deal on Aug. 1 and went 4-1 with a 2.48 ERA in eight starts with Las Vegas.
The Mets promoted outfielder Darrell Ceciliani and placed him on the 60-day disabled list to clear the 40-man roster spot for Stauffer. The Mets recently performed similar roster maneuvers with Wilfredo Tovar and Jack Leathersich to open 40-man roster spots.
Manager Terry Collins expects Torres to conservatively miss at least a week or two.