The 26-year-old, who played a part in six of Australia's matches on their run to the final at last year's World Cup, will be out for six weeks, Brumbies assistant coach Dan McKellar told reporters in Canberra on Friday.
Toomua, a hard-tackling inside centre with a prodigious boot, suffered the injury in last weekend's loss to the Otago Highlanders in Invercargill.
Michael Cheika has indicated that overseas-based players will not be selected for the series but Toomua's likely absence might force the Australia coach to consider calling up Matt Giteau from French Top 14 side Toulon.
The series against England begins in Brisbane on June 11 and continues with tests in Melbourne and Sydney on the following two Saturdays.
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(Reporting by Nick Mulvenney; Editing by Mark Lamport-Stokes)
