Those arrested are believed to have come from China’s Xinjiang region with ties to the attacker, Anadolu agency says.
Deputy PM Veysi Kaynak also said they were closing in on the attacker, who he said was possibly an ethnic Uighur.
Also on January 5, there was an explosion near the courthouse in the city of Izmir in western Turkey.
Social media images showed two vehicles ablaze and several people were reported wounded.
Other images showed what appeared to be the body of a man carrying a gun, amid media reports he was an attacker who was shot dead by police.
Anadolu reported a second man was shot dead and police were seeking a third.
ISIS says it carried out the Istanbul attack over Turkey’s military involvement in the Syrian civil war.
Turkish authorities have reportedly tightened security at the country’s land borders and airports to prevent the attacker from fleeing abroad.
Local media have run images of a suspect, saying the pictures were handed out by the police. But the police have given no official details.
The Turkish foreign minister has said the authorities have identified the gunman, but has not given further details.
Special forces made the early morning arrests at a housing complex in Selimpasa, a coastal town on the outskirts of Istanbul, after police were reportedly tipped off that individuals linked to the attacker were in the area.
Uighurs were among those detained – the number was not confirmed – on suspicion of “aiding and abetting” the attacker, Anadolu reported.
At least 36 people were already in custody over suspected links to the attack, many of whom were picked up in an earlier police operation in Izmir.
Several families had recently traveled there from Konya, a central city where the main suspect was said to have stayed for several weeks before the attack.
Separately, Veysi Kaynak told Turkish broadcaster A Hamer that the authorities knew where the suspect, who he described as “specially trained”, was hiding, without giving further details.
The deputy prime minister confirmed the attacker had acted alone, but may have had help inside Reina club.
Veysi Kaynak expressed confidence in the Turkish police operation but said he could not rule out the possibility of the attacker fleeing the country.
Previous media reports incorrectly suggested the attacker was a national from Kyrgyzstan, after a passport photo claiming to show the gunman was circulated.
It later emerged the passport belonged to someone unrelated to the attack.
Kyrgyzstan’s embassy in Turkey has since asked the media to retract the reports and issue an apology.
More than half of those killed in New Year’s attack on Istanbul’s popular Reina club were foreigners, including citizens from Lebanon, Saudi Arabia, Israel, Iraq and Morocco.
The gunman managed to escape in the aftermath of the attack.
A day later, ISIS issued a statement saying “a heroic soldier” belonging to the group had carried out the attack in retaliation for Turkey’s military role in northern Syria.
Veysi Kaynak also said on January 5 Turks were questioning the use of the country’s Incirlik air base by both NATO and the US-led coalition launching air strikes on ISIS in Syria and Iraq.
Turkey launched a military operation in Syria in August to push back ISIS and Kurdish forces.
Some of Turkey’s big cities have since been targeted in a number of bomb attacks by ISIS and by Kurdish militants.
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