"During the combat operations in the direction of the Tovuz region, the stronghold of another company of the armed forces of Armenia was destroyed by the accurate fire of our units", the statement said.
The ministry also posted video footage of the operation on its website.
The head of the ministry's press service, Col. Vagif Dargyakhly, stated earlier in the day that the Azerbaijani side had destroyed an Armenian military facility and equipment near Tovuz.
Clashes broke out in the border area that separates Armenia's Tavush province and the Azerbaijani region of Tovuz on Sunday and have continued into their third day. Baku and Yerevan have accused one another of provoking the conflict, which is taking place a reasonable distance away from the disputed territory of Nagorno-Karabakh, where the two sides have waged war for decades.
A total of 11 Azerbaijani troops have so far died during the violence, according to reports from Baku. On the other side, four Armenian servicemen have lost their lives in the recent escalation.