Two Iranian guards were also wounded in the clash Saturday, it said, adding the fighting started after Iranian border security forces entered the western province of Nimroz.
"An Afghan civilian who was a teacher was killed in a clash between Afghan and Iranian border guards. The fighting took place after the Iranians entered and claimed a piece of land," the ministry said in a statement.
It did not say how much land the Iranians had claimed except that it was not large and added that the Afghan owner, who was using it for farming, had documents proving his ownership.
The Afghan troops sealed off the area and forced their Iranian counterparts to "escape," the ministry said.
The Iranians had left behind a vehicle which was returned to them, it said.
The long border between the two countries is porous and difficult to police. It has seen clashes before, sometimes related to the trafficking of Afghanistan's mammoth drugs production across the frontier.
