Drew, 34, suffered the injury while running out a ground ball on April 11 against the St. Louis Cardinals after his cleat caught in the dirt near the batter's box.
Drew appeared in eight games before the injury, going 4-for-18 (.222) with one double, three runs scored and four RBIs.
In 2016, Drew was valuable coming off the bench when he hit .324 with one double, one triple, four home runs, seven RBIs, eight runs scored and three walks. Overall, he hit .266 with eight home runs and 21 RBIs in 70 games.
The Nationals also optioned left-hander Matt Grace to Triple-A Syracuse to make room on the roster for Drew.
Grace, 28, has a 4.05 ERA in seven appearances out of the Nationals' bullpen this season.