The procedure was to repair a torn ligament, a right wrist injury he sustained in the team's loss to the Baltimore Ravens on Nov. 16.
"The procedure went as planned and he is expected to make a complete recovery," the team said in a statement. "Joe will return to Cincinnati this week to be with the team and begin the recovery and rehab process."
Earlier on Monday, Bengals coach Zac Taylor was hesitant to share details on Burrow's surgery until it was completed. Taylor did say that Burrow wanted to be around the team in Cincinnati as he continues to recover for his season-ending injury.
"We'll see how he comes out of this," Taylor told reporters in Cincinnati on Monday. "Maybe there's some soreness there and he wants some time to himself. But he and I had a good conversation last week and he wanted to be very involved going forward."
The Bengals (5-6) have dropped three straight games. Jake Browning made his first career start in the loss to the Steelers.
Cincinnati, which has won the AFC North and reached the conference championship game the last two years, is looking to make the postseason for the third straight year.