Gunfire directed toward fighters in the landlocked Nagorno-Karabakh region from Azerbaijani forces on Tuesday morning killed the fighter, the ministry stated.
At least 110 people died in days of clashes between forces supported by Azerbaijan and Armenia earlier this month amid tensions over the disputed territory.
A shaky Moscow-brokered ceasefire kicked off on April 5 and stopped the huge fighting but the two sides still continue to accuse one another of violating the truce.
The new wave of unrest in Karabakh and surrounding areas in Azerbaijan have sparked concern about resumption of hostilities in the strategic region, which has been relatively calm since the end of a three-year war in 1994.
Fears are also high that the war could trigger a broader conflict in the Caucasus region between Russia and Turkey.
A fortnight ago, Russia’s foreign minister urged Turkey to stop what he called meddling in the internal affairs of other countries.
Sergei Lavrov said Ankara was “one-sided” in supporting its ally Baku in the old territorial dispute.
Nagorno-Karabakh is a landlocked region in the South Caucasus, lying between Lower Karabakh and Zangezur and covering the southeastern range of the Lesser Caucasus mountains. The region is mostly mountainous and forested.
The region is internationally recognized as part of Azerbaijan; however, it is governed by the self-proclaimed Nagorno-Karabakh Republic, a nation established on the basis of the Nagorno-Karabakh Autonomous Oblast of the Azerbaijan Soviet Socialist Republic.