The Scot was forced off 15 minutes from time as the Black Cats fell to a 3-0 defeat at the Hawthorns in what turned out to be Paolo Di Canio's final game in charge of the club.
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"The news is better than we expected," Ball told reporters. "Hopefully, it will be four to six weeks, which is great news."
Fletcher was the club's top scorer last season, with 11 goals, but missed the end of the campaign with an ankle problem that required surgery.
The injury also saw him miss the start of the new season, finally making his long-awaited return as a substitute against Crystal Palace, scoring in a 3-1 defeat at Selhurst Park.
The Black Cats take on Liverpool on Sunday and will also be without striker Fabio Borini, who is ineligible to face his parent club, with Sunderland going into the game bottom of the table with just one point from five games.