Two girls, aged nine and 15, were among those killed when the bomb exploded shortly after 4:00 pm (1300 GMT) on Sunday in Istiklal Avenue, home to smart boutiques and European consulates. More than 80 other people were wounded.
"The person who planted the bomb has been arrested," Interior Minister Suleyman Soylu said in a statement broadcast by the official Anadolu news agency early Monday.
"According to our findings, the PKK terrorist organisation is responsible," Soylu said.
The PKK, blacklisted as a terrorist group by Ankara and its Western allies, has waged a deadly insurgency for Kurdish self-rule in southeastern Turkey since the 1980s.
It denied any role in the latest attack.
"Our people and the democratic public know closely that we are not related to this incident, that we will not directly target civilians and that we do not accept actions targeting civilians," the group said in a statement published by the Firat news agency, close to the PKK.
Police, quoted by private NTV television, said the chief suspect is a Syrian woman working for Kurdish militants. Forty-six people were detained in total, police said.
Police footage shared with Turkish media showed a young woman in a purple sweatshirt being apprehended in an Istanbul flat.
Police, cited by NTV, named her as Alham Albashir and said she was arrested at 02:50 am in an Istanbul suburb. Local media said she was a trained PKK intelligence operative.
"Order from Kobane"
There has been no claim of responsibility.
"We believe that the order for the attack was given from Kobane," Soylu said, referring to a city in Syria near the Turkish border.
PKK-affiliated Kurdish militants control most of northeastern Syria and in 2015, Kurdish fighters drove Islamic State jihadists out of the city.
Turkey's NTV channel also shared surveillance footage of a young woman dressed in trousers and wearing a loose black scarf who ran away into the crowd on Sunday afternoon.
Justice minister Bekir Bozdag told A Haber television that a woman had been sitting on a bench for more than 40 minutes, "then she got up", leaving a bag.
"One or two minutes later, an explosion occurred," he said.
On Monday, all the benches had been removed from Istiklal Avenue, where residents laid red carnations at the scene of the blast, some wiping away tears and others speaking of their fear of further attacks in the run-up to elections next June.
"We need more security!" said Idris Cetinkaya, who works at a nearby hotel and who came to pay his respects.
"Live with fear"
"The police just searched my bag when I got here, but that's the first time in a year. Millions of people come here, anything could happen at any second!"
Istiklal Avenue was previously targeted during a campaign of nationwide bombings in 2015-16 that were blamed mostly on the Islamic State group and outlawed Kurdish militants, killing nearly 500 people and wounding more than 2,000.
On Sunday, Turkish President Recep Tayyip Erdogan denounced the "vile attack" that had the "smell of terror" shortly leaving for the G20 summit in the Indonesian resort island of Bali.
Kemal Ozturk, a shopkeeper, is among those who fear another explosion ahead of presidential and legislative elections in seven months' time.
"In election period it can happen," the 42-year-old told AFP. "We live with fear".
Regularly targeted by Turkish military operations, the PKK has also been at the heart of a tussle between Sweden and Turkey, which has blocked Stockholm's bid to join NATO since May, accusing it of leniency towards the group.
Reject US condolences
International condemnation flooded in from across the world, including from the United States, but on Monday Turkey said it rejected US condolences over the attack.
Erdogan's government has often accused Washington of supplying weapons to Kurdish fighters in northern Syria who Ankara labels as terror group linked to the PKK.
"We do not accept the US embassy's message of condolences. We reject it," Soylu said.
"We stand shoulder-to-shoulder with our NATO ally Turkey in countering terrorism," said White House Press Secretary Karine Jean-Pierre. The US embassy tweeted it was "deeply saddened by the explosion".
President Vladimir Putin on Monday added his own condolences in a message to Erdogan.
"We reaffirm our readiness for the closest interaction with our Turkish partners in the fight against all forms and manifestations of terrorism," he said in the telegram.
Istiklal Avenue reopened Monday to pedestrian traffic.
"My son was there. He called me and said an explosion happened," said Mecit Bal, who runs a small shop a few metres from the scene.
He will not go back to work today. He is psychologically affected," he told AFP.