It said an Armenian UAV "attempting to carry out reconnaissance flights" over Azerbaijani positions in the Terter frontline area was destroyed.
Baku also said due to drone's "poor" quality, it was unable to harm Azerbaijani troops.
"The Ministry of Defense warns that adequate retaliatory actions will be devastating for the enemy," it added.
The two countries remain in dispute over the occupied Karabakh region, which pro-Armenian militia took over in 1993.
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.
