Escobar suffered the injury during a bizarre play in the top of the first. He stole second base and advanced to third on a throwing error by catcher Matt Treanor.
Royals center fielder Melky Cabrera tried to get Escobar at third only to have his throw bounce away from Mike Aviles. That allowed Escobar to score the game's first run.
Escobar, who has appeared in 59 of Toronto's 61 games this season, is currently listed as day-to-day.
"He took a charlie horse on the slide to second base," Blue Jays manager John Farrell said after Toronto's 8-5 victory. "He got kneed by the middle infielder there and we will have to evaluate him [Wednesday] whether he's good to go.
"We tried to nurse him through it a little bit but as each inning progressed, he felt some additional soreness and tightness in there so we got him out."
Utilityman Mike McCoy entered the game and likely will start at shortstop on Wednesday if Escobar is unable to go. Toronto is also currently playing without infielder John McDonald, who is on the 15-day disabled list with a right hamstring strain.
Escobar entered Tuesday's game hitting .284 with seven home runs and 24 RBIs. He has reached base safely in 48 of his 59 games this year and is tied for second in on-base percentage (.364) among American League shortstops.