Afghan officials alleged that Pakistani forces were trying to build a security post on the border in Maruf area of Kandahar province along Balochistan and started firing when Afghan security forces objected to the construction.
Kandahar police spokesman Ziaur Rehman Durrani told media that one police officer was killed in the clash which lasted for about two hours.
Pakistan and Afghanistan share an over 2,600-kilometre controversial and porous border known as the Durand Line named after Henry Mortimer Durand, the then foreign secretary of British India, who demarcated it in 1893.
Clashes frequently occur over construction of border posts.
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Last year in May, Afghan forces foiled an alleged attempt by Pakistan to build a post on the border in Mohmand tribal district, injuring four Pakistani soldiers.
A Pakistani security official has meanwhile rejected the Afghan official claim that any new construction is being carried out by Pakistani troops inside Afghan territory in Qila Saifullah, near Chaman in Balochistan.
The official said Afghan National Army troops resorted to unprovoked firing on the Pakistani post this morning in Loe Bund area near Qila Saifullah.