Kluivert had scored Bournemouth's first-ever European goal in Anoeta, but picked up an injury, manager Marco Rose revealed on Sunday.
"Justin suffered an injury in San Sebastian. We're gonna miss him for some weeks. Nothing real bad, but it needs time," Rose said.
The injury will cost Kluivert the upcoming UEFA Nations League games with the Netherlands, where Xavi will make his debut as Oranje manager against Germany on September 24th.
In addition to Kluivert, Roma's Donyell Malen will be absent for Xavi's maiden Netherlands games.
Xavi has replaced the pair with PSV midfielder Guus Til and AZ striker Mexx Meerdink. Til, an 8-time Netherlands international, scored twice in PSV's 3-2 loss against FC Twente on Sunday, while the uncapped Meerdink has scored three goals and provided two assists for Eredivisie leaders AZ so far.
The Netherlands will open their UEFA Nations League campaign against Germany, after which they'll face Greece and Serbia twice.
