Escobar suffered the injury while running from first to third on a single by Colby Rasmus in the third inning. It flared up again in the fourth as Escobar attempted to beat out a ground ball to second base.
The 29-year-old Escobar tried to remain in the game, but he was removed in the fifth because of lingering soreness.
"He's day-to-day at this point," Blue Jays manager John Farrell said. "He was examined, he's got some groin issue going on. We just have to be precautionary with what he's got taking place right now."
The Blue Jays were forced to shift around their defensive alignment to accommodate the departure. Jose Bautista moved from right field to third base, Brett Lawrie went from third to shortstop, while Rajai Davis entered the game to play in right.
Escobar is hitting .262 with two home runs and 15 RBIs in 46 games this season. The native of Cuba is the second Blue Jays middle infielder to go down in as many days with second baseman Kelly Johnson also being out because of soreness in his left hamstring.