Escobar was injured during the fourth inning when New York's Francisco Cervelli slid into his glove during a stolen-base attempt.
The 28-year-old Escobar is currently listed as day to day. The injury had drawn comparisons to the one suffered by outfielder Colby Rasmus, which required a stint on the 15-day disabled list, but that's not expected to be the case with Escobar.
"[Escobar] said it doesn't feel too bad today, but we'll re-evaluate it tomorrow," Blue Jays acting manager Don Wakamatsu told reporters on Sunday.
"Initially, we don't think it's near what Rasmus' was. I think Rasmus knew the two incidents that happened were a little bit more severe."
Toronto recalled veteran Chris Woodward from Triple-A Las Vegas to provide more depth around the infield during Escobar's absence. The club was not required to make a corresponding move because rosters were expanded on Sept. 1.
Woodward hit .296 with 13 home runs and 65 RBIs in 108 games for the 51s. He also spent four games with Toronto earlier this season but didn't record a hit in four at-bats.
Left fielder Eric Thames also was left out of the Blue Jays starting lineup because of flu-like symptoms. He eventually did get into Sunday's 9-3 loss to the Yankees in the ninth inning as a pinch-hitter but struck out.
"The report I got at the end of the game [on Saturday] was kind of viral," Wakamatsu said. "Just felt sick and still a little weak today, so we'll re-evaluate him again tomorrow, too."