The Northern Ireland midfielder was withdrawn midway through the second half of last Saturday's 3-0 home defeat to Manchester United.
And, following a diagnosis of medial knee ligament damage, Brunt is set to miss much of West Brom's fight against relegation from the Premier League.
West Brom are yet to win a game under the stewardship of new head coach Pepe Mel, who has a number of other injury concerns heading into the trip to Swansea City this weekend.
Midfielder Claudio Yacob is a doubt due to a hamstring problem, while defender Steven Reid has a knee injury and could also be unavailable.
Full-back Billy Jones is making progress in his recovery from a hamstring tear picked up in the 1-1 draw with Fulham last month, however, centre-back Diego Lugano faces three to four weeks on the sidelines after suffering a similar injury to Brunt while on international duty with Uruguay.
West Brom travel to the Liberty Stadium on Saturday out of the relegation zone by virtue of goal difference only.
