Anderson, who is out indefinitely, tweeted about the surgery Friday morning and called it a "super success."
If the Broncos elect to put Anderson on injured reserve, he has to be out for at least six weeks before he can return to practice and has to be out for a minimum of eight weeks before he can play in a game.
Anderson suffered the injury during an 11-yard run on the final play of the first quarter of the Broncos' 27-9 victory over the Houston Texanson Monday night. As he closed in on Texans cornerback A.J. Bouye, Anderson tried to make a cut just before contact, planted his right foot and his knee buckled slightly as he then was tackled.
He sat on the field for several moments after the play, talking to the Broncos' trainers, and at one point grabbed his lower right leg. Anderson returned to the game in the second quarter, with a 3-yard run eight plays later.
Anderson finished the game with 107 yards on 16 carries.
"He played in the game. He played through it,'' Broncos coach Gary Kubiak said.
Rookie Devontae Booker, who had 83 yards rushing against the Texans on Monday night, will start Sunday's game against the San Diego Chargers. Kapri Bibbs will be the No. 2 running back, and the Broncos have Juwan Thompson, who has been on the roster the previous two seasons, on the practice squad.
The Broncos matched an $18 million offer sheet to Anderson from the Miami Dolphinsthis offseason. Anderson has 437 yards rushing this season to go with four rushing touchdowns.
ESPN staff writer Jeff Legwold contributed to this report.