The 26-year-old Neath man went off in the 23rd minute of the Ospreys 27-19 derby win over the Scarlets on Friday.
And with the Heineken Cup quarter-final Biarritz in San Sebastian looming large, coach Sean Holley admits losing the Wales international is a blow.
“He is a tough cookie so it’s quite serious, early indications aren’t great,” Holley told the BBC.
Hibbard won four caps for Wales in 2007 but has been troubled with the same knee injury since January and this kept him out of contention when hooker injuries struck Wales in the Six Nations.
Hibbard was replaced in the match against the Scarlets by Huw Bennett who must now be the favourite to start against the Basques.
