Tomane was injured in a clash with Crusaders flanker Matt Todd late in the Brumbies' 40-14 humbling in Canberra and will be sidelined for up to eight weeks, the team said.
With five tries, the 26-year-old was the Brumbies' top try-scorer this season and in line for a spot in Michael Cheika's squad for the three-match series against England.
The series opens in Brisbane on June 11, with matches in Melbourne and Sydney in following weeks.
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Tomane's loss is a heavy blow for the Brumbies, who were knocked out of top spot in the Australian conference by the Crusaders defeat and head to Invercargill this weekend to take on champions the Otago Highlanders.
Co-captain Stephen Moore is also in doubt for the Highlanders game after suffering a heavily bruised thigh, making Wallabies flanker David Pocock's return from a two-game suspension all the more important.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
