Selahattin Demirtas of the Peoples' Democratic Party (HDP) was in his armoured vehicle in the mainly Kurdish southeastern city of Diyarbakir late Sunday when it was hit by a single bullet at head height, the party said in a statement.
However the governor's office of the Diyarbakir region denied that he had been the target of an assassination attempt or that the car was hit by gunfire.
Demirtas "survived the assassination attempt unharmed thanks to the bullet-proof vehicle (in which) he was riding," the HDP said on its official Twitter feed.
The pro-Kurdish Firat news agency said that neither Demirtas nor his guards had heard a shot being fired but noticed the bullet mark when getting out of the car at the end of the journey.
"A bullet mark was found at head level of the rear window of the official vehicle," Demirtas told Firat, without giving further details.
There was also no indication that any bullet or cartridge had been found at the scene.
On his official Twitter feed, Demirtas simply sent a five word tweet in Kurdish reading "my death is Allah's command", implying his fate was in the hands of God.
Meanwhile the hashtag #DemirtasYalnizDegildir (Demirtas you are not alone) became a trending topic in Turkey.
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Prominent HDP MP Sirri Sureyya Onder told the Hurriyet daily that the car could have been targeted while parked earlier simply in order to intimidate the Kurdish leader.
- 'No kind of attack' -
In a statement, the governor's office of Diyarbakir said the car had been examined by the authorities and a mark three centimetres (1.2 inches) in width and height had been found on the rear window.
But it said there was no evidence it was caused by "any kind of firearm" and it had in fact been produced by a "collision with a very hard object".
The statement said that Demirtas had been given police protection throughout his stay in Diyarbakir and during this time "no kind of attack against him or against his vehicle has been realised".
The incident comes with tensions riding high in Turkey between the authorities and the Kurdish minority as the government presses a four-month offensive against the banned Kurdistan Workers Party (PKK).
Kurdish militia forces have meanwhile been battling Islamic State (IS) jihadists for control of northern Syria.
There have been three deadly attacks since June on pro-Kurdish activists blamed on IS, including the October 10 suicide bombings on a peace rally in Ankara that killed 103.
One of Turkey's most charismatic politicians, Demirtas has won supporters for the HDP outside its main Kurdish base and has become a major rival of President Recep Tayyip Erdogan.
His co-chair at the top of the HDP, Figen Yuksekdag had said in October that the HDP had information of assassination plots against her and Demirtas.