Local residents reported the sound of gunfire by the Torkham crossing and said people around the busy border area near the Khyber Pass had fled once the firing started.
Security officials from the area, who spoke on condition of anonymity, said that Taliban and Pakistani forces had exchanged fire but there had not yet been any casualties.
A spokesman for the local government in Afghanistan's Nangahar province, where the crossing is located, and a spokeswoman for Pakistan's foreign office did not immediately respond to request for comment.
Disputes linked to the 2,600 km (1,615 miles) border have been a bone of contention between the neighbours for decades.
The crossing has been closed several times in recent years, including a closure in February that saw thousands of trucks laden with goods stranded on each side of the border for days.
