Kenyan national police spokesman Bruno Shioso said journalist Arshad Sharif was fatally wounded by an officer after his car drove through a police barrier in the Magadi area, 40 kilometers from the capital Nairobi.
"It is then that they shot at, fatally injuring late Arshad Mohammed Sharif," he said in a statement, adding that the journalist was travelling with a man described as his "brother" Khurram Ahmed.
"National Police Service regrets this unfortunate incident," he said.
According to a police report seen by AFP, the car carrying the two men was struck by around nine bullets, but continued on to the home of another Pakistani national.
There, Sharif was found to be dead "with a gunshot wound on the head which had penetrated from the back.
"I lost friend, husband and my favourite journalist today, as per police he was shot in Kenya," Sharif's wife Javeria Siddique tweeted.
In a phone call with Kenyan President William Ruto, Pakistan's Prime Minister Shehbaz Sharif called for a transparent investigation into the late-night shooting on Sunday.
In a post on Twitter, Pakistan PM Sharif said he had asked Ruto to "ensure fair & transparent investigation into shocking incident. He promised all-out help including fast-tracking the process of return of the body to Pakistan."
In August, the journalist had interviewed senior opposition politician Shahbaz Gill, who said junior officers in Pakistan's armed forces should not follow orders that went against "the will of the majority".
The comment led to the news channel being briefly taken off air and an arrest warrant issued for Sharif, who fled the country.
The channel ARY later said it had "cut ties" with him.
Media rights group Reporters Without Borders (known by its French acronym RSF) said Sharif had been shot dead with two bullets in "unclear circumstances" and urged an international investigation into "this gruesome and utterly disturbing murder".
The killing was "all the more baffling since he had just left his home country to Kenya in order to escape harassment and arrest", it added on Twitter.
RSF's call was echoed by the Kenya Editors' Guild which said those responsible should be brought to book.
"This would not only demonstrate Kenya's and the government's ability to protect its citizens and visitors but also assure Kenyans and the international community that Kenya is safe for everyone, including journalists whose rights it should protect."