The 26-year-old suffered ligament damage while on international duty with Scotland against Wales, and he will now target a return to full fitness for the start of next season.
The 26-year-old is the Black Cats' leading scorer this season with 11 goals following his 12 million pound summer move from Wolves, but he has missed the last three games after landing awkwardly in his country's World Cup qualifier against Wales in March.
The club has not yet set a timeframe on how long Fletcher's recovery period will be, but it confirmed that he had undergone a procedure on his injured ankle on Monday. Since the striker's injury, the Mackems have replaced manager Martin O'Neill with Paolo Di Canio and gone on to beat local rivals Newcastle 3-0 at St James' Park as they continue their fight against relegation.
Sunderland remains just three points above the drop zone in 15th position, with Wigan holding a game in hand over, as well as 16th-placed Stoke and 17th-placed Aston Villa.
Fletcher last found the net against QPR in March, though that goal proved ineffective as the Black Cats lost 3-1 on the day.