Anderson suffered the injury earlier this month while warming up for a bullpen session. Montoyo declined to say who would fill the fifth spot in the Blue Jays' rotation to start the season.
The 32-year-old Anderson joined the Blue Jays in November when he was traded by the Milwaukee Brewers for a prospect. Milwaukee had planned to decline his $8.5 million option, which would have made him eligible for salary arbitration. Toronto exercised the option after the trade.
Anderson was 8-4 with a 4.21 ERA in 27 starts and five relief appearances last season.
Ryu signed a four-year, $80 million contract with the Blue Jays this offseason. He was among the best pitchers in the National League in 2019, going 14-5 with an NL-best 2.32 ERA for the Los Angeles Dodgers, whom he had played for since 2013.
The Blue Jays open the regular season with five road games against the Rays and Washington Nationals. They have not yet established where they will play home games, starting July 29 against the Nationals, after the Canadian government denied them permission to play in Toronto this season.