29-year-old journalist Ahmad Shah has been working in the BBC's Afghan service for more than a year. He was also Reuters journalist.
Khawat provincial governor's spokesman Talib Mangal said that Ahmad Shah was hit by the attack on his way to Gulzar area on the outskirts of Khost.
Local residents said that gunmen attacked him when Shah was on bicycle. The injured Shah was taken to the hospital after his death.
The BBC confirmed its death in a statement on Twitter.
At least 26 people, including nine journalists, were killed in a blast in Afghanistan's capital, Kabul on Monday, killing at least one journalist.
A week before the gunmen killed an Afghan journalist in the southern Afghan city of Kandahar.
There is no evidence of any direct link between these two killings.