The Scotland international was helped off the pitch after landing heavily when attacking a cross in the 3-0 defeat at West Brom last Saturday, which proved to be Paolo Di Canio's last game in charge as manager.
An assessment of the injury has confirmed that the former Wolves man is set to spend a significant amount of time on the sidelines, although the lay-off will not be as long as originally anticipated.
"The news is better than we feared," caretaker boss Kevin Ball said.
"It's four to six weeks which is good news for us. I've been downstairs and Steven has a smile on his face; albeit he realises that it's four to six weeks.
"Hopefully he'll be back within that time and he'll be a great addition to the squad."
Despite Fletcher's absence, Sunderland do boast a number of attacking options with Jozy Altidore, Connor Wickham, Ji-Dong Won and Fabio Borini all available to Ball.
Borini is ineligible to face Liverpool on Sunday as part of the conditions of his loan, a fixture that marks the beginning of a difficult run for Sunderland, who will also face Manchester United, Swansea City and local rivals Newcastle United in the next month.
Sunderland are still searching for a successor to Di Canio, with former Brighton and Hove Albion manager Gustavo Poyet the favourite to take over.
