"On the evening of March 11 (Wednesday) an Armenian army reconnaissance group attempted an attack on Azerbaijani positions and was repelled after fierce fighting," Azerbaijan's defense ministry said in a statement.
"An Azerbaijani army serviceman was killed in action."
Baku and Yerevan have been in a decades-long dispute over Azerbaijan's Nagorno-Karabakh region since a bloody war in the early 1990s.
Ethnic Armenian separatists backed by Yerevan seized control of Karabakh and another seven adjacent districts of Azerbaijan during the conflict that left some 30,000 dead.
Despite years of negotiations, the two sides have not signed a final peace deal, with Armenian-populated Karabakh still internationally recognized as part of Azerbaijan, although no Azeris remain on the territory.
Threatening a shaky 1994 truce, clashes between Azerbaijani and Armenian forces intensified again in January following an unprecedented spiral of violence last year.
At least 16 people from both sides were reported killed and 18 wounded this year in sporadic flare-ups on the Armenian-Azerbaijani border, and along the Karabakh frontline.
Baku, whose military spending exceeds Armenia's entire state budget, has threatened to take back the territories by force if negotiations fail to yield results, according to AFP.
Armenia, which is heavily armed by Russia, says it could crush any offensive.