Turks as well as visitors from several Arab nations, India and Canada were among those killed in the attack.
The suspect was caught in a special operations raid at a housing complex in Esenyurt district, on the European side of the city.
There were three people in the apartment where he was caught, the home of a Kyrgyz friend of his to which he had gone three days earlier, Haberturk said.
According to state-run Anadolu news agency, five people were detained in the operation, including the alleged perpetrator, a man of Kyrgyz origin and three women. It said simultaneous raids were being conducted on other cells linked to the group.
The shooting in Istanbul's Ortakoy neighbourhood, an market district on the Bosphorus shore, came after a year in which Nato member Turkey was shaken by a series of attacks by radical Islamist and Kurdish militants and by a failed coup.
One security source said in the wake of the attack that the gunman appeared to have been well-versed in guerrilla warfare and may have trained in Syria.
President Tayyip Erdogan said the attack, which targeted a club popular with local celebrities and foreigners, had been exploited to try to divide the largely Sunni Muslim nation.
Dogan news agency published what it said was the first image of the attacker. It showed a bruised, black-haired man in a grey, bloodied shirt being held by his neck. Private NTV television said the gunman had resisted arrest.
Hurriyet said the alleged gunman's wife and 1-year old daughter were caught in a police operation on January 12.
Police established the suspect's whereabouts four or five days ago, but delayed the raid so they could monitor his movements and contacts, NTV reported.
The television channel also broadcast footage showing plain-clothed police taking away a man in a white top and sweat pants, forcing his head down. The station said the images showed the gunman's Kyrgyz friend being taken to a police vehicle.
The state-run Anadolu Agency likewise reported the arrest and identified the gunman, only with a slightly different spelling of his first name, Abdulgadir.
Turkish Foreign Minister Mevlut Cavusoglu posted a Twitter message thanking the Interior Minister, Suleyman Soylu, police and intelligence organisations "who caught the Reina attacker in the name of the people".
Earlier in the day, Turkish Deputy Prime Minister Numan Kurtulmus said the Reina nightclub attack had been carried out professionally with the help of an intelligence organisation, a claim he had made in the first days after the attack. He did not name the organisation suspected of being involved.
- Telegraph Group Ltd, AP