Baku said the solider was killed due to provocations by Armenia's armed forces and that full responsibility lies with Yerevan's political and military leaders.
An Azerbaijani soldier has died in a shootout with Armenian forces, two weeks after both countries held talks on easing tensions following their war last year.
Azerbaijan's Defence Ministry said on Thursday one of its soldiers "was killed overnight as a result of a provocation by Armenia's armed forces" near the countries' shared border.
"Full responsibility for the escalation lies with Armenia's political and military leaders," the ministry said in a statement.
Last autumn, the ex-Soviet Caucasus neighbours fought a six-week war over occupied Karabakh which claimed more than 6,500 lives.
Hostilities ended last November with a Russian-brokered ceasefire under which Yerevan ceded swathes of territory it had occupied for decades.
READ MORE: Clashes stop at Azerbaijan, Armenia border
Armenian Prime Minister Nikol Pashinyan and Azerbaijani President Ilham Aliyev met for rare face-to-face talks under the mediation of Russian President Vladimir Putin last month.
The talks focused on resolving disputes left over from last year's war, and were hailed by all sides as positive.
They also addressed the issue of rebuilding Soviet-era transport links between Azerbaijan and Armenia which are currently closed by a mutual blockade.
The trio met less than two weeks after the worst fighting since the Karabakh war killed six Armenian troops and seven Azerbaijani soldiers.
On December 4, Azerbaijan freed 10 Armenian soldiers it had captured during border clashes last month.
Aliyev and Pashinyan are to meet again in Brussels on December 15 for talks mediated by the European Council President Charles Michel.
Relations between Azerbaijan and Armenia have been tense since 1991 when the Armenian military occupied Karabakh region, also known as Upper Karabakh, a territory internationally recognised as part of Azerbaijan, and seven adjacent regions.