The left-back fell awkwardly on his left arm in the second half of Napoli's 3-1 second-leg play-off-round defeat in Bilbao, condemning the Italians to a 4-2 aggregate loss.
Napoli confirmed that the 23-year-old is to undergo a minor corrective surgical procedure on the injury and will now also be unable to feature in Algeria's upcoming Africa Cup of Nations qualifiers with Ethiopia and Mali.
Ghoulam has made 22 appearances for Napoli since joining from French side Saint-Etienne in January.
Napoli, who travel to Genoa on Sunday, will go into Friday's Europa League draw.
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