The bomber detonated his explosive vest after walking up to Ghayur's vehicle when it stopped at a traffic light near his office.
Ghayur, an upright and bold officer who personally led many operations against militants, had received several threats to his life.
Taliban spokesman Tariq described the attack as an act of "revenge" for Ghayur's role in operations against militants.
"We killed him, he was our target...all such officers who are active against us will suffer the same fate," he said.
Speaking from an undisclosed location, Tariq said, "We shall continue to target law enforcement personnel and leaders of the ruling Awami National Party."
He said the security personnel and ANP leaders were "on our hit-list".
The Taliban recently gunned down the only son of senior ANP leader Mian Iftikhar Hussain, who is also the Information Minister of Khyber-Pakhtunkhwa province.
Hussain is an outspoken critic of the Taliban and their tactics, including suicide attacks.