Neither Addai, who is currently being held out of practice sessions, nor team officials, would divulge which knee underwent the procedure.
A team official told ESPN.com that he was "very confident" Addai will recover in time for training camp.
Addai also reiterated that his rehabilitation is going well. "It's feeling good right now," Addai said.
The team's first-round choice in the 2006 draft, Addai is coming off an injury-filled 2008 season. The former LSU star started 12 games, and carried 155 times for 544 yards and five touchdowns. All represented career lows for Addai.
It marked the first time Addai had failed to rush for 1,000 yards in a season, and his 3.5-yard average was nearly a full yard less than his career average entering the 2008 season.
It was also the second consecutive year in which Addai's rushing yardage declined. He ran for a career-best 1,089 yards as a rookie in 2006, despite not starting any games and sharing time with Dominic Rhodes. Addai rushed for 1,072 yards in 2007.
Although he has been the Colts' starter since 2007, Addai typically has shared the tailback spot with a second player. The Colts invested their first-round choice this year in Donald Brown, and the former Connecticut star is expected to spell Addai -- and, in the eyes of some, contend for the starting job.
"He's working through a bit of a rehab situation, but he's in fine physical condition," Colts coach Jim Caldwell said of Addai. "He's been lifting, doing all the things that have been required of him."
Len Pasquarelli is a senior NFL writer for ESPN.com.