De Bruyne suffered the injury when scoring the opening goal from the penalty spot, with the Belgium international immediately clutching the back of his right thigh before he was helped off the pitch.
Scans later revealed a "high-grade lesion to the biceps femoris muscle", prompting the need for surgical intervention.
"As planned, Kevin De Bruyne underwent surgery today in Antwerp following a high-grade injury to his right thigh biceps femoris muscle," Napoli said in a statement.
"The operation was a complete success. De Bruyne... will continue the first phase of his post-surgical rehabilitation in Belgium."
Napoli did not provide a timeframe for the 34-year-old's return. De Bruyne has a history of hamstring problems and also underwent surgery in 2023 when he was with Manchester City.