Fellow starting pitcher Steven Matz, meanwhile, underwent tests on his left arm that confirmed that he is dealing with a nerve issue but showed no structural damage. Matz, who is 3-2 with a 3.86 ERA this season, was scheduled to start Wednesday's game against the San Diego Padres but likely will miss that start.
Vargas left his start against the Milwaukee Brewers on Sunday after four innings because of mild hamstring tightness.
He is 1-2 with a 5.92 ERA in 24 1/3 innings pitched this season.
In other moves Monday, the Mets activated left-hander Justin Wilson (elbow) from the injured list, recalled right-hander Corey Oswalt from Triple-A Syracuse and optioned right-hander Tim Peterson to Triple-A.