The 31-year-old Schultz initially was diagnosed with bone chips in his right elbow, but manager John Gibbons hinted that Tommy John surgery was a possibility as well.
"He's got a couple of chips in there and they'll look at the ligament while they're in there," Gibbons said before Schultz underwent the procedure.
Schultz had been in the mix for one of the final two spots in the bullpen. Aaron Loup and Mike Bolsinger appear to be the favorites to win the jobs in the final week of camp, but right-hander Ryan Tepera is still in the running as well.
Schultz made 16 appearances for the Blue Jays last season, posting a 5.51 ERA. He was hampered by a hip injury, but he was a key contributor in the bullpen in 2015, when he had a 3.56 ERA over 43 innings.