Leach, who took four wickets in England's 10-wicket win over Ireland in a one-off test earlier this week, has been an ever-present in England's squad under coach Brendon McCullum and captain Ben Stokes (32), claiming 45 test wickets last year.
He was included in the 16-man squad for the first two Ashes tests announced by England on Saturday.
Leach's injury is the latest major setback to England's bowling department in the build-up to the series, with fast bowler Jofra Archer (28) also ruled out.
"The Somerset slow left-armer developed low back symptoms during England's victory over Ireland on Saturday," the ECB said in a statement.
"A scan on Sunday in London has revealed a stress fracture, which will keep him out of the forthcoming Ashes test series ... England will announce a replacement for the Ashes series in due course."
The Ashes gets under way at Edgbaston on June 16th.
