The school said in a statement that the injury stemmed from a "non-basketball related trauma."
"Allen is one of our top players and top players in the SEC," coach Bruce Pearl said. "I'm disappointed for him but know he will do everything in his power to get back and lead us this season."
A 6-foot-6 wing, Flanigan averaged 14.3 points, 5.5 rebounds and 2.9 assists last season, shooting 33.8% from 3-point range. He had six 20-point outings, including 22 points in a season-finale victory over Mississippi State.
Flanigan is ranked No. 19 in ESPN's 2022 NBA draft rankings, the second-highest-ranked returning college player.
"It's an unfortunate situation, but I trust that God has a plan," Flanigan said. "I'm going to work hard to get back stronger and better than ever."
Without Flanigan for the first one to two months of the season, Devan Cambridge is expected to take on a bigger role after starting 19 games last season and averaging 8.9 points. Newcomers Jabari Smith and Walker Kessler are expected to start up front, while transfers K.D. Johnson (Georgia), Wendell Green Jr. (Eastern Kentucky) and Zep Jasper (Charleston) will battle for minutes in the backcourt.
Auburn is ranked No. 22 in ESPN's most recent Way-Too-Early Top 25. The Tigers open the season against Morehead State on Nov. 9.