Major Jawad Chengazi succumbed to his injures at Combined Military Hospital (CMH), the army said.
Changezi was injured yesterday. He is the third fatality from the artillery exchanges.
Two Afghan policemen were killed and nine others wounded in gunfights since Sunday.
On Pakistani side, 18 people, many of them civilians, were wounded.
Pakistan yesterday summoned a top Afghan diplomat after security forces of the two countries exchanged gunfire over the contentious fencing issue at the border crossing.
Last month, the border crossing was sealed for several days over the construction of the gate, causing hardships to thousands of people who cross it every day.
Afghan government does not recognise the border, which is also known as Durand Line, and it opposes permanent structure.
