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."
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)
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