The team said Monday night Perez will get a second opinion before a course of action is determined. Tommy John surgery is often recommended for similar injuries.
Blue Jays starter Kyle Drabek is already out for the year after tearing the same ligament in his right elbow. He underwent Tommy John surgery last month.
The 27-year-old Perez was placed on the 15-day disabled list Sunday with left elbow tightness. He left Toronto's 11-9 win over the Chicago White Sox with a team trainer in the seventh inning after giving up hits to Alex Rios and Alexei Ramirez.
He went 2-2 with a 3.43 ERA in 35 appearances this season.