The Suns termed Friday's surgery by team doctor Thomas Carter a success. No timetable was given for Bledsoe's return, but the team said in a news release that he "will pursue a possible return to action during the second half" of the season.
Bledsoe was having the finest season of his career after being acquired by the Suns from the Los Angeles Clippers in the offseason, averaging 18 points and 5.8 assists per game.
He and Goran Dragic formed the double-point guard backcourt that had been the catalyst of the Suns' surprising start.
This is the second time in a little more than three years that the 24-year-old player has undergone surgery to repair a torn meniscus in the same knee. The first surgery was performed Oct. 7, 2011, during the lockout of that NBA season.
The Suns, who lost 104-99 at Memphis on Friday night, are one of the NBA's most surprising teams with a 21-14 record. They now are 16-8 with Bledsoe and 5-6 without him. He missed six games earlier this season with a bruised shin and was sidelined the four games before Friday's announcement with what the team initially said was a sprained right knee.
The injury puts more pressure on Dragic, who is averaging 19.1 points and 5.9 assists per game. To bolster the depleted backcourt, Phoenix signed Leandro Barbosa to a 10-day contract this week. The 31-year-old Brazilian, who also is coming off knee surgery, had his best NBA seasons with the Suns, including winning the league's Sixth Man Award in 2007 after averaging 18 points a game. Barbosa scored four points in his return Friday night.
Gerald Green moves into the starting lineup in Bledsoe's absence. Green, who made the winning shot in Wednesday night's victory at Minnesota, was acquired, along with center Miles Plumlee, in a trade that sent Luis Scola to Indiana.
"It's tough," Green told azcentral sports at the team's Friday shootaround in Memphis. "You lose a player like that, playing at the high level he's been playing at, it's going to be tough. This team is made for the next-man-up mentality."
Bledsoe's offense, particularly his lane penetration, has been a critical part of his success, but his defense probably will be more sorely missed.
"Guys are going to have to step it up," Suns coach Jeff Hornacek told azcentral sports. "It's unfortunate that he's going to miss some games but I think the more they'll get used to the rotation, hopefully that'll make us better."
The injury comes at a tricky juncture in Bledsoe's career financially. He will become a restricted free agent at the end of this season, and while the Suns have indicated they would match any offer for him, it's possible that two knee surgeries in his first four NBA seasons might diminish his value, at least somewhat.
The team's Memphis stop was the third on a five-game trip.