The Armenian Foreign Ministry said the pilot of the Soviet-made SU-25 died after being hit by the Turkish F-16 in Armenian airspace.
Turkey, which supports Azerbaijan in the conflict, has denied the allegation.
Nearly 100 people, including civilians, have died in three days of fighting in the disputed mountainous region.
The mountainous enclave is officially part of Azerbaijan, but has been ruled by ethnic Armenians since 1994.
The fighting that started three days ago now appears to be spreading out of Nagorno-Karabakh.
Armenia and Azerbaijan – which have already mobilized more troops and declared martial law in some areas – blame each other for starting the fighting.
There are growing concerns that other countries are directly involved in the conflict in the strategic Caucasus region.
While Turkey supports Azerbaijan, Russia – which has a military base in Armenia – called for an immediate ceasefire.