Fiji-born Speight had just recovered from an eye socket injury he sustained in Super Rugby in late March, only to suffer a grade three medial ligament injury to his right knee in a practice match on Tuesday.
"We're all gutted for Henry. He made a commitment to the programme and has done everything he possibly could to get himself in the frame for Olympic selection," Australia coach Andy Friend said in a news release.
"Even after the facial injury he received some ten weeks ago, Henry's commitment didn't waver but the rugby gods just haven't been kind to him whatsoever."
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Australia will name their men's and women's teams for the inaugural Olympic rugby sevens tournaments on July 14.
The Rio Olympics take place from Aug. 5-21.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
