Murphy left Thursday night's game against the Arizona Diamondbacks in the third inning with a tight quad after he tried to beat out a grounder.
Eric Campbell replaced Murphy at third. The Mets have called up Daniel Muno, who has bounced between Triple A and the majors this season, to take Murphy's place on the roster.
Murphy is batting .283 with a team-high 29 RBIs this season.
The injury comes against a backdrop of other recent debilitating Mets injuries.
Mets star third baseman David Wright, who has not played at all during the 2015 season due to a spinal injury, announced Tuesday he would not have surgery at this time to repair the injury, but did not provide a timetable for his return.
Murphy, who has played primarily as a second baseman in the majors, has been playing third base in Wright's absence.