The Packers now must decide whether to keep Rodgers on the roster or put him on injured reserve.
Even if they put Rodgers on IR, he could still return after eight weeks.
On Friday, Packers coach Mike McCarthy said the team is discussing long-term options for Rodgers.
Rodgers's surgery was performed out of town and McCarthy said "everything went well." McCarthy said Rodgers will not be at the game on Sunday against the Saints.
"He's in recovery mode," McCarthy said.
This is a different course of action than four years ago, when Rodgers broke his left clavicle. He did not undergo surgery then and missed seven games. The Packers went 2-4-1 using three different quarterbacks in Rodgers' absence in 2013. Rodgers returned for the regular-season finale -- a game the Packers won to make the playoffs.
Brett Hundley will make his first NFL start Sunday against the Saints at Lambeau Field. Hundley threw one touchdown and three interceptions in relief of Rodgers against the Vikings.
NFL Network first reported Rodgers' surgery.