Marte left Wednesday's game against the Colorado Rockies after attempting to beat a throw to first base.
Marte crumpled to the ground after passing the base and trainers helped him off the field.
Manager Torey Lovullo said postgame that Marte felt his leg cramping as he ran down the baseline, according to Nick Piecoro of the Arizona Republic.
The 27-year-old entered Wednesday as one of the league's hottest hitters. Through the first five games of the season, Marte was batting .522 with two home runs over 25 plate appearances. He went 0-for-3 before the injury forced him out of the contest in the sixth.
Arizona recalled utility man Andrew Young from the taxi squad to replace Marte on the active roster.