Drabek, who underwent ligament replacement surgery as a minor leaguer in 2007, will visit noted surgeon Dr. James Andrews on Monday to confirm the diagnosis.
The former first-round pick left Wednesday's start against the Washington Nationals in the fifth inning after a "popping" in the back of the elbow.
The Blue Jays placed Drabek on the 15-day disabled list earlier Friday, calling the injury a sprain, before general manager Alex Anthopoulos revealed the tear later in the afternoon, before Toronto's game against the Philadelphia Phillies.
Drabek is 4-7 with a 4.67 ERA in 13 starts.
Drabek became the second Blue Jays starter in three games to leave injured when he walked off in the fifth inning Wednesday. Right-hander Brandon Morrow left Monday's game after just nine pitches with a strained muscle in his left side, and is also on the 15-day DL.
Things got even worse for Toronto when rookie right-hander Drew Hutchison left with an apparent injury just nine pitches into Friday's start against the Phillies.
"It's always tough," Anthopoulos said before the game. "You realize it can happen. No one is going to feel sorry for you, we've seen injuries across the game. They finally hit us in the middle of June, but hopefully we have some guys who come up and do a good job for us."
Toronto recalled left-hander Brett Cecil from Triple-A Las Vegas to replace Drabek. Cecil will make his season debut Sunday against the Phillies, taking Morrow's turn in the rotation. It's not yet known who'll start when Drabek's turn in the rotation comes up Tuesday when Toronto plays at the Milwaukee Brewers.
"You can't overreact," Anthopoulos said. "We're still going to try and make a run at it."
Toronto's loss to Washington on Wednesday dropped the Blue Jays to 31-32, below .500 for the first time this season.
Drabek was one of three minor leaguers acquired by the Blue Jays in the trade that sent right-hander Roy Halladay to Philadelphia in December 2009.
Phillies manager Charlie Manuel said he was disappointed to hear that Drabek, Philadelphia's first-round pick in 2006, may have to undergo a second surgery, sidelining him for a year or more.
Strength tests on Drabek's elbow performed after his departure from Wednesday's game showed no problems. Anthopoulos said Drabek's is "an odd case" because the 24-year-old is not in any pain, a sentiment echoed by manager John Farrell.
"The MRI shows an injured ligament and yet at the same time his symptoms aren't consistent with a tear," Farrell said. "You would have a guy that would either have swelling or he would be very sore when you go through a range of motion or you put some stress on the elbow to test the ligament. That could speak to his overall strength of the muscles that support the elbow. But still, there is something that's definitive in there."
Anthopoulos said some pitchers are able to keep throwing despite minor ligament tears, but that the Blue Jays wanted him to see Dr. Andrews for further diagnosis.
"There's guys all over the game that have tears and can throw with it," Anthopoulos said. "So from that standpoint, we just need to make 100 percent sure."
Anthopoulos conceded that a second surgery was a possibility for Drabek.
"There's no question he might have to go down that path," Anthopoulos said.