Sullivan underwent surgery by Dr. James Andrews on his left knee on Tuesday at St. Vincent's Hospital in Birmingham. Auburn officials said there is no timetable for his return.
"I feel for Frankie and the Auburn family," Barbee said. "We were all looking forward to him having a big year.
"I'm a big believer in things happening for a reason even though we don't always understand why," Barbee said. "We know Frankie will use his toughness and work ethic to come back 100 percent and will rejoin the team when he is fully healthy.
"I am glad the surgery was a success, and we look forward to him completing his rehab and getting back on the court and helping the team," Barbee added.
The 6-1 guard averaged 12.7 points, 3.7 rebounds and 2.0 assists per game last season as a sophomore.