The jihadist group made the claim in a statement on one of its Telegram channels, a method it has used to claim attacks in the past. There was no immediate comment from Turkish officials.
At least five Saudis killed in Istanbul nightclub attack
"In continuation of the blessed operations that Islamic State is conducting against the protector of the cross, Turkey, a heroic soldier of the caliphate struck one of the most famous nightclubs where the Christians celebrate their apostate holiday," the statement said.
NATO member Turkey is part of the US-led coalition against Islamic State and launched an incursion into Syria in August to drive the radical Sunni militants from its borders.
The authorities believe the assailant may be from a Central Asian nation and suspect he had links to Islamic State, Turkey's Hurriyet newspaper said. Police distributed a hazy black-and-white photo of the alleged attacker taken from security footage.
Turkey 'Santa' nightclub attack: What we know
The shooting at the Reina nightclub on the shores of Istanbul's Bosphorus waterway shook Turkey as it tries to recover from a failed July coup and a series of deadly bombings in cities including Istanbul and the capital Ankara, some blamed on Islamic State and others claimed by Kurdish militants.
Some people jumped into the Bosphorus to save themselves after the attacker began shooting at random just over an hour into the new year. Witnesses described diving under tables as he walked around spraying bullets from an automatic rifle.
Erdogan says Istanbul nightclub attack sought to create chaos in Turkey
Nationals of Saudi Arabia, Morocco, Lebanon, Libya, Israel, India, a Turkish-Belgian dual citizen and a Franco-Tunisian woman were among those killed, officials said. Saudi newspaper al-Riyadh said five of the dead were from Saudi Arabia.
Security services had been on alert across Europe for new year celebrations following an attack on a Christmas market in Berlin that killed 12 people. Only days ago, an online message from a pro-Islamic State group called for attacks by "lone wolves" on "celebrations, gatherings and clubs".
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