Rose, a three-time All-Star who was named the NBA's Most Valuable Player last year, suffered the knee injury in Chicago's opening play-off game last month.
Doctor Brian Cole, who performed the operation on Saturday, said Rose was facing a lengthy break from the game.
"The time frame that we believe an athlete of this calibre generally requires is about eight to 12 months. Sometimes shorter, sometimes longer," he said.
"While he will be in hopefully a very high level in eight to 12 months, it still may take slightly longer for him to be at his pre-injury level, that's not uncommon in athletes at this calibre."
At best, Rose would miss the first few months of the 2012-13 NBA season, starting at the end of October. At worst, he could miss the entire campaign, which could be a major blow to the Bulls.
They finished the 2011-12 regular season as the number one ranked team in the Eastern Conference but, without Rose, they bowed out of the play-off race in the first round when they lost to the Philadelphia 76ers.