The 24-year-old suffered the injury towards the end of the FA Cup fifth-round victory over MK Dons and missed the midweek win over Wolves.
A scan confirmed the extent of the damage and he went under the knife on Thursday morning.
Tykes boss David Flitcroft told the club's official website: "It's a massive blow because his form has been incredible.
"I'll sit down with Scott at some point and we'll through his objectives for pre-season."
Golbourne had made 35 appearances for the club this season, scoring once in the 3-2 win at Middlesbrough.
