"At dawn, a military patrol operating in Remada, which was carrying out its normal duties in the border buffer zone, was targeted by sudden fire from an unknown source," the ministry said in a statement.
Remada is in the far south of the country.
The attack "resulted in the death of a soldier from the military patrol," it added.
The ministry said it hadn't identified the shooter, but an investigation has been opened.
Smugglers have been active in the area while the presence of jihadist groups is growing.
In 2013, Tunisia established a buffer zone along the border which civilians are not permitted to enter.
Tunisian military forces often carry out operations in mountainous and desert areas along the borders with Libya and Algeria.
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