Urdapilleta tore his hamstring in his side's 33-19 Top 14 defeat to last season's beaten Heineken Cup finalists ASM Clermont Auvergne at the Stade Marcel Michelin at the weekend.
An Argentine international, Urdapilleta has previously played Amlin Challenge Cup rugby for Harlequins, although he has featured just once for Oyonnax in this season's competition.
The 27-year-old won't be available for the games against Biarritz Olympique and Worcester Warriors on January 11 and 18 respectively as Oyonnax look to finish their first European season on a high.
Oyonnax have won one, drawn one and lost two of their four Pool 1 ties this term, with their solitary victory coming over pool leaders Sale Sharks in Round 3 when Urdapilleta was in the starting line up.
They were thumped 53-14 by Sale last time out, though, and cannot now qualify for the quarter-finals given that they are 10 points behind the Sharks and nine adrift of Biarritz, with the top two teams playing each other in the last round.
But while their own hopes of a place in the last eight have already been wiped out, Oyonnax can still have a say on who qualifies from the pool. Avenging their Round 2 defeat to Biarritz and preventing the Basque outfit from picking up a losing bonus point in the process would mean that a maximum point success for Sale against Worcester would see the Sharks wrap up the pool with a round to spare.