Bresnan starred with both bat and ball as England beat Australia by 74 runs in the fourth Test against Australia at Chester-le-Street on Monday as they went 3-0 up with one to play and so won a third straight Ashes series.
He took the key wicket of David Warner to pave the way for Stuart Broad's match-winning spell.
"England and Yorkshire pace bowler Tim Bresnan has been ruled out of the remainder of the international season with a stress fracture in his lower back," an ECB statement said.
"Bresnan will begin a recovery and rehabilitation programme and a date for his return to cricket will be determined in due course."
The first England match Bresnan will miss is next week's fifth and final Test against Australia at The Oval in south London starting on Wednesday, August 21.