The Fiji-born back suffered the injury, which may require surgery, when he clashed heads with team mate Christian Lealiifano during the ACT Brumbies' Super Rugby loss to the Stormers in Cape Town on Saturday.
"It’s a shame to lose Henry, he’s obviously a world-class winger," Brumbies head coach Stephen Larkham said in a news release.
"At this stage it looks like he may be out for eight weeks, which would be around the same time we take on the Rebels in Round 12, but we will have to wait for further advice."He's remaining positive and will be doing everything he can to get back on the field as soon as possible."
Speight's injury also looks likely to rule him out of all but the final two rounds of the World Sevens series in Paris and London in May, a major blow to his hopes of proving he could adapt to the shorter game.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The 27-year-old made his World Series debut in Dubai last December and also featured in the inaugural Sydney Sevens in early February.
Larkham said the Brumbies already had contingencies in place to replace Speight after he decided to have a go at making the Australia sevens team for the Olympics.
Winger Lausii Taliauli will join the squad in South Africa, while outside backs Nigel Ah Wong, Robbie Coleman and James Dargaville were already available to Larkham for Saturday's match against the Cheetahs in Bloemfontein.
(Reporting by Nick Mulvenney, editing by Peter Rutherford)
