Bichette was held out of the team's Sunday doubleheader against the Tampa Bay Rays.
Bichette could be facing a long layoff.
Rob Longley of the Toronto Sun reported that "the injury is worse than first feared and Bichette could be out of the lineup until mid-September. That prognosis could change after further diagnosis and treatment and Bichette is renowned for his work ethic, but the team is expecting a lengthy absence."
Montoyo said Bichette suffered the injury while stretching before going to hit Saturday, but he didn't say anything until after the rain-shortened game.
"We lost at this point one of the best players in baseball, the way he was hitting the ball," Montoyo said Sunday. "Somebody's going to have to pick up the slack. It's a big loss losing Bo."
The 22-year-old Bichette is an emerging star, hitting .356 this year with five homers, 13 RBI, 11 runs and four stolen bases in 13 games. He is also in the midst of an eight-game hitting streak and has settled nicely into the No. 2 spot in the lineup.
"It's tough," Anthony Alford said. "He's a big bat in our lineup, and he's been swinging the bat really well. But at the same time, we've got other guys in the lineup who can hit."
Joe Panik and Brandon Drury could each see time at shortstop in Bichette's absence.