According to the news agency, the attack took place on the eve of a presidential election that Taliban insurgents have pledged to disrupt through a campaign of bombings and assassinations. (Agencies)
The news agency said photographer Anja Niedringhaus, 48, had been killed and reporter Kathy Gannon, 60, wounded while they were sitting in their car.
Niedringhaus, an internationally acclaimed German photographer, was killed instantly, according to an AP Television freelancer who witnessed the shooting.
Canadian reporter Kathy Gannon, who is based in Islamabad and has covered war and unrest in Afghanistan for 30 years, was wounded twice and was receiving medical attention, the new agency said.
She was described as being in stable condition and talking to medical personnel, it said.
"Anja and Kathy together have spent years in Afghanistan covering the conflict and the people there. Anja was a vibrant, dynamic journalist well-loved for her insightful photographs, her warm heart and joy for life. We are heartbroken at her loss," AP Executive Editor Kathleen Carroll, speaking in New York, told the agency.
The two journalists were in a remote small town on Afghanistan's border with Pakistan when the attack took place.
Taliban attacks on security forces and civilians have been on the rise since the start of the year ahead of Saturday's vote when Afghans will elect a successor to President Hamid Karzai who is barred by the constitution from running again.
The assault on the journalists came just weeks after an Afghan journalist with the Agence France-Presse news agency was killed alongside eight other people when Taliban gunmen opened fire inside a luxury hotel in the centre of the capital, Kabul.
Also in March, a gunman shot dead Swedish journalist Nils Horner, 51, outside a restaurant in Kabul.
The news agency said Niedringhaus and Gannon were travelling in a convoy of election workers delivering ballots from the centre of Khost city to the outskirts, in Tani district.
The area borders Pakistan's lawless North Waziristan region where many al Qaeda- and Taliban-linked militants are based.
The two had arrived in a heavily guarded district compound shortly before the attack. As they were sitting in the car waiting for the convoy to move, a unit commander walked up to the car, yelled "Allahu Akbar" â€” God is Great â€” and opened fire on them with his AK-47, the news agency said.
He then surrendered to the other police and was arrested.
Word of Niedringhaus's death interrupted a U.N. briefing in Geneva, where she was based. A former colleague proposed a minute of silence, and several of her friends paid tearful tributes.
"She was supposed to be ironclad, this just seems so incredibly wrong," said Jonathan Fowler, a correspondent at AFP who previously worked with Niedringhaus at the news agency.
According to the news agency, the attack took place on the eve of a presidential election that Taliban insurgents have pledged to disrupt through a campaign of bombings and assassinations.