Interior Minister Suleyman Soylu told Turkey's state Anadolu news agency on Monday that the person who planted the bomb that killed several people on Sunday had been arrested.
"A little while ago, the person who left the bomb was detained by our Istanbul Police Department teams," Soylu was quoted as saying.
"According to our findings, the PKK terrorist organisation is responsible," he added, referring to the Kurdistan Workers' Party (PKK) and by extension its Syrian branch the Democratic Union Party (PYD).
At least six people were killed and 81 injured Sunday by the bombing, according to Turkish authorities.
Turkish President Recep Tayyip Erdogan said the blast was a "vile attack."
"It would be wrong to say this is undoubtedly a terrorist attack but the initial developments and initial intelligence from my governor is that it smells like terrorism," he told a news conference.
Turkish Vice President Fuat Oktay later said he assumed the blast was a "terrorist attack" that appeared to have been carried out by a woman.
Anadolu reported that five prosecutors were assigned to investigate the cause of the blast.
What happened in the Istiklal street explosion
Videos shared on social media showed multiple people on the ground amid blast damage. The footage showed an ambulance and police arriving on the scene.
Turkish media reports indicated the blast occurred at 4:20 p.m. local time (1330 GMT). Video posted online taken at the time of the blast showed a fireball overwhelming the crowded street as pedestrians strolled before abruptly turning, many running scared.
"I was 50-55 meters (yards) away, suddenly there was the noise of an explosion. I saw three or four people on the ground," witness Cemal Denizci, 57, told AFP news agency. "People were running in panic. The noise was huge," he said.
On social media, users said Istiklal Street, just off Taksim Square, was cordoned off as shops were closed. A Reuters news agency reporter observed a helicopter over the blast scene.
Turkey's media watchdog, the Supreme Board of Radio and Television, imposed temporary restrictions on reporting about the blast and its aftermath shortly after the incident. In the past, such restrictions have been in place following similar incidents.
Istiklal Street runs through the central district of Beyoglu, home to many foreign residents and is frequented by tourists. Previously in 2016, a suicide bomber detonated on Istiklal, killing four and injuring 39.
Turkey's ongoing conflict with the Kurds
Ankara's claim that Kurdish militants were behind Sunday's attack come amid a decadeslong conflict between Turkish forces and the leftist PKK.
In recent years the conflict has spread into Kurdish held regions of northern Syria parts of which were invaded and occupied by Turkey. Ankara has also repeatedly banned pro-Kurdish political parties and has imprisoned key Kurdish political figures.
Soylu further claimed that "the instruction for the attack came from Kobani," the Syrian Kurdish city on the Turkish border that made headlines for resisting an onslaught by IS forces in 2015.
Erdogan has threatened to once again send Turkish troops into Syria to fight the US-backed Kurdish groups despite warnings from Washington, Moscow and Tehran against such a move.
Soylu also laid blame on the US, comparing a message of condolence from the White House to a "killer being first to show up at a crime scene."
World leaders react to the Istanbul explosion
German President Frank-Walter Steinmeier expressed his condolences to Erdogan. "My thoughts are with the victims and their families, and my wishes for recovery go out to all those injured." Steinmeier wrote Sunday, according to a statement from his office.
"In this moment of shock, we Germans stand by the citizens of Istanbul and the Turkish people."
German Foreign Minister Annalena Baerbock also said: "My thoughts are with the people who simply wanted to stroll on the Istiklal shopping street on a Sunday and have now become victims of a serious explosion."
"Our thoughts are with those who were injured and our deepest condolences go to those who lost loved ones," a White House statement said. The statement said that the US stood "shoulder-to-shoulder" with Turkey in fighting terrorism.
French President Emmanuel Macron expressed his condolences on Twitter.
"On this meaningful day for our nation, just as we commemorate those who lost their lives on November 13, 2015, the Turkish people were attacked from their heart, from Istanbul," Macron said, referring to attacks on the Bataclan theater and other parts of Paris claimed by the so-called "Islamic State" militant group seven years ago.
"We share your pain. Our condolences. We are with you in the fight against terrorism," he said.
ab, fb, ar/aw (AP, AFP, dpa)