Rasmus aggravated the injury during a game against the Yankees on Aug. 10. He was originally expected to make his return against Chicago on Tuesday night but became a late scratch a few hours prior to first pitch.
"We might have to look to get him in a DH slot initially," Blue Jays manager John Farrell said of Rasmus' eventual return. "Just running him back into the lineup on both sides of the ball right now is maybe a little too aggressive.
"Want to be sure that he's feeling good about himself and confident from a physical standpoint before running him back out there. But after we went through the work yesterday, thought today might be the day, but we'll hold him out one more day."
The Blue Jays did receive some encouraging news about right fielder Jose Bautista on Tuesday. The veteran slugger took dry swings and hit off a tee on Monday and the did not experience any lingering effects from the workout.
Bautista has been out since July 16 with inflammation in his left wrist. He went through another day of tee work on Tuesday and is scheduled for an off-day from workouts on Wednesday. There is still no timetable for his return but the pain appears to have subsided at least for now.
"Didn't feel it yesterday," Farrell said of the pain. "Before being shut down previously, he felt like he was guided by some discomfort and I think his gut feel at that time was that he had to be cautious. Yesterday was symptom free so the additional down days did him some good."
Bautista is hitting .244 with 27 homers and 65 RBIs in 90 games while also posting an .894 OPS.