Davis initially twisted his ankle during a rundown between first and second on April 1. He missed two games before returning to the Blue Jays' lineup on April 5.
Since that time, Davis made six starts in center, but the soreness resurfaced following Saturday night's 14-inning game that lasted more than five hours.
"I think the  innings didn't help," said Davis, who was removed from Sunday's game in the fifth inning. "Then with such a quick turnover, playing an early game, day game, not much time to rest it. Really tough on it when it's still healing."
The Blue Jays remain hopeful that Davis will not require a stint on the 15-day disabled list. He will rest for a couple of days, while recently activated outfielder Corey Patterson likely assumes the starting job in center.
After leading Toronto in home runs during Spring Training, Davis has had a slow start to the regular season. The 30-year-old is hitting just .156, with one stolen base and four runs scored.
Blue Jays manager John Farrell thinks the main reason behind that lack of success has been the nagging ankle soreness.
"You can see he's not really driving off the backside, particularly at the plate," Farrell said. "To his credit, he keeps going out there, giving it every thing that he's got. But it's to the point now where it is affecting his game."
Travis Snider took Davis' spot in center field. It was the first time in Snider's Major League career that he played a position other than the corner outfield spots.