The 34-year-old sustained the injury while celebrating a wicket in the second of three One Day Internationals last week, so did not play in the third.
England lost all three so are 6-0 behind on the points-based system, meaning they need to win all the remaining games to regain the urn. The only Test, worth four points, is due to take place for four days from Thursday in Taunton, Somerset.
The teams then play three Twenty20 matches. In the second ODI, Brunt took one for 27 off seven overs as Australia chased 217 with four wickets remaining. She missed the third match on Sunday, in which England were dismissed for 75 chasing 269.