According to a statement by Azerbaijan's Defense Ministry, the unmanned aerial vehicle (UAV) was destroyed on Saturday evening.
The incident happened on the line of contact between Azerbaijani and Armenian troops in Azerbaijan’s Fuzuli region.
Azerbaijan and Armenia remain in dispute over the occupied Karabakh region.
Karabakh broke away from Azerbaijan in 1991 with Armenian military support and a peace process has yet to be implemented.
Armenia and Azerbaijan fought a six-year war over occupied Karabakh in the early 1980s until a 1994 ceasefire.
Since the end of war in 1994, Armenia and Azerbaijan have held talks under the supervision of the Organization for Security and Co-operation in Europe’s Minsk Group.
An agreement-in-principle was reached in St. Petersburg, Russia, following talks late June involving Azerbaijani President Ilham Aliyev, Russian President Vladimir Putin and Armenian President Serzh Sargsyan.
This April, according to the Azerbaijan Defense Ministry, more than 270 military personnel were killed in the worst breach of a 1994 treaty between the sides.
Three UN Security Council Resolutions (853, 874 and 884), and United Nations General Assembly Resolutions 19/13 and 57/298 refer to Karabakh as being part of Azerbaijan.
The Parliamentary Assembly of the Council of Europe refers to the region as being occupied by Armenian forces.