"Bresnan will begin a recovery and rehabilitation programme and a date for his return to cricket will be determined in due course," the England and Wales Cricket board said in a statement on its website (www.ecb.co.uk) on Thursday.
The Yorkshire all-rounder helped England win the Ashes outright after taking a 3-0 series lead with victory over Australia in the fourth Test at Chester-le-Street on Monday.
He is likely to be replaced by fast bowler Chris Tremlett for the fifth Test at the Oval starting on Wednesday.
Graham Onions, who would have been another candidate to come in, has been ruled out with a broken finger meaning England are unlikely to be able to rest main strike bowler James Anderson.
Swing specialist Anderson started the Ashes in fine form but was upstaged by team mate Stuart Broad in the fourth Test where he looked tired.
Bresnan will also miss two Twenty20 internationals against Australia at the end of this month and the five one-day internationals in September.
England will hope he is fully fit for the reverse Ashes series starting in Australia in November.
Image: Tim Bresnan
Photograph: Gareth Copley/Getty Images
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