Speight, 27, suffered the injury in a collision of heads with team-mate Christian Lealiifano in the first half of Brumbies' 31-11 loss to Stormers in Super Rugby on Saturday.
Brumbies' Henry Speight to miss eight weeks
Australia and Brumbies wing Henry Speight is out for up to two months due to a fractured bone above his eye.
Brumbies coach Stephen Larkham was saddened by the injury to the five-time Wallaby.
"It's a shame to lose Henry, he's obviously a world-class winger," he said.
"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."
As Speight flies back to Canberra, Lausii Taliauli has gone to South Africa to link up with the Brumbies squad.
Speight is looking to play for Australia in the Sevens at the Rio Olympics, and should still have enough time to secure his place.
Brumbies, who hold a 3-1 win-loss record this season, face Cheetahs in Bloemfontein on Saturday.
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