The ministry said in a statement an Armenian X-55 drone had been detected flying over the front line between Azerbaijani and Armenian forces.
It said the incident happened in the Agdam region but did not provide information on when it was shot down.
The ministry also released photographs of the drone.
The Azerbaijani army destroyed five Armenian drones last year: one in April, one in November and three in December.
The two countries remain in dispute over the occupied Karabakh region.
Clashes in the region, which pro-Armenian militia took over in 1993, are nothing new.
In April 2016, more than 270 military personnel lost their lives in the worst-ever breach of a 1994 treaty between the sides, according to the Azerbaijani Defense Ministry.
Three UN Security Council Resolutions (853, 874 and 884), and United Nations General Assembly Resolutions 19/13 and 57/298 refer to Karabakh as part of Azerbaijan. The Parliamentary Assembly of the Council of Europe refers to the region as being occupied by Armenian forces.