Cole was pulled from the game in the fourth inning after allowing a sacrifice fly to Reese McGuire that gave the Blue Jays a 3-1 lead over the Yankees.
After the play ended, Cole motioned to the dugout and was examined by Yankees trainer Tim Lentych. Albert Abreu then replaced Cole in the contest.
Cole gave up three runs -- two earned -- and five hits across 3 2/3 innings, tossing 70 pitches in his outing. He recorded two strikeouts, tying the Philadelphia Phillies' Zack Wheeler for the MLB lead (217).
The 30-year-old Cole entered Tuesday's game with a 14-6 record and 2.73 ERA this season. He had a 4-0 mark and 0.73 ERA in four starts since missing time after a positive COVID-19 test.
Cole struck out 15 over seven innings during his start against the Los Angeles Angels on Wednesday.
Entering Tuesday, the Yankees were second in the American League East with a 78-59 record. New York trailed the first-place Tampa Bay Rays by 8 1/2 games.