The Scotland international dislocated his shoulder during last Saturday's 3-0 Premier League defeat at West Brom, and there were concerns that he could be sidelined for several months.
However, interim head coach Kevin Ball revealed on Friday afternoon that the latest prognosis is much more positive.
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."
Former Hibernian forward Fletcher, who was the Black Cats' top scorer with 11 goals last season, missed the end of last season and the start of the current campaign after undergoing ankle surgery.