The decision was taken after Kluivert visited Amsterdam to seek specialist advice and he was told he had little option but to go under the knife
Valencia doctor Antonio Giner said Kluivert will remain in the Netherlands until the operation.
The Netherlands international, 29, has played just 217 minutes of league soccer this season since joining Valencia from Newcastle United in June. He left Tyneside under a cloud, complaining Graeme Souness didn't have the bottle to drop Alan Shearer and play him with Craig Bellamy, which he described as a "far better partnership".
Prior to his problems at St James' Park, he had a horror season at Barcelona when he was dropped and the Spanish giants tried for months to offload him.