"We've got to treat the heck out of it today, get back in there, treat it and hopefully he's available on Tuesday," Blue Jays pitching coach Pete Walker said.
Cecil hasn't pitched since leaving in the eighth inning of Toronto's win against the Orioles on Friday with the injury.
With Cecil injured, the Blue Jays are limited to just one lefty -- Aaron Loup -- out of the bullpen.
Toronto has a day off on Monday, after which the team hopes Cecil will be able to return. If not, the Blue Jays will have to reach a decision soon about whether to place Cecil on the disabled list. Toronto is currently using a two-man bench after first baseman Adam Lind suffered a right foot contusion during the Blue Jays' 3-2 loss on Saturday.
"He felt pretty good today," Walker said of Cecil. "Definitely encouraging."
David Wilson is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.