Chung exited the game in the third quarter and didn't return after suffering a broken right forearm while tackling Rams running back Todd Gurley.
The veteran safety, who had his arm in a sling, took to Instagram on Friday to share an update after his successful procedure.
"Surgery is good, fellows," Chung said. "I'm right back, I'm right back."
Sources told NESN and the Boston Globe that Chung will undergo more than one surgery this offseason. Chung will also have shoulder surgery in about three weeks, cleaning up a shoulder injury he played through during last season.
Chung played 85 percent of the Patriots' defensive snaps in the 2018-19 season. He served as a utility defender for the team, switching between safety, linebacker and the nickel corner spot.
Chung saw action in 15 regular-season games and recorded 84 total tackles, one interception, three passes defensed and 0.5 sacks. He added 13 total tackles and one pass defensed in three playoff games during New England's run to its sixth Super Bowl title in 2018-19.