Rodgers was injured in the first quarter of last Sunday's 23-10 loss at Minnesota after taking a hard hit from Vikings linebacker Anthony Barr.
Though the Packers placed Rodgers on IR, they still could bring him back after eight weeks and give him a chance to return for the Week 15 game at Carolina on Dec. 17.
Packers coach Mike McCarthy indicated that was one of the discussion points prior to the decision being announced.
"We're actually discussing all the long-term options at this point," McCarthy said. "The focus has been on Aaron's health, making sure everything went well with the surgery and those discussions will continue."
The 33-year-old Rodgers will not attend Sunday's game at Lambeau Field against the New Orleans Saints as he recovers, but McCarthy said "everything went very well" with the surgery.
Rodgers posted a picture on Instagram on Thursday night from his hospital room after the surgery.
"Surgery went well," Rodgers wrote. "Thanks for all the love, support, thoughts and prayers. #comebackstartsnow #riseagain."
Rodgers previously broke his left non-throwing collarbone in Week 9 in 2013, remaining on the roster and returning after seven weeks. He did not undergo surgery after that injury and returned for the regular-season finale as the Packers won at Chicago to capture the NFC North and a playoff spot.
This season, Rodgers has completed 128 of 193 passes (66.3 percent) for 1,385 yards with 13 touchdowns and three interceptions. He was the NFL's MVP in 2011 and 2014, and he led the Packers to the Super Bowl XLV title after the 2010 season.
Backup quarterback Brett Hundley will make his first NFL start on Sunday for the Packers, who are tied with the Vikings at 4-2 for first place in the NFC North.
Hundley was intercepted three times and sacked four times after replacing Rodgers. Hundley finished 18 of 33 for 157 yards and one touchdown.
Starting right tackle Bryan Bulaga cleared the NFL's concussion protocol on Friday and left tackle David Bakhtiari (hamstring) was able to practice on a limited basis. Both could play Sunday.