[1] A youth academy graduate of Urartu, Melkonyan made his senior team debut on 4 March 2017 in a 2–1 league defeat against Alashkert.

[2] On 13 May 2023, he scored his team's winning goal in the 2023 Armenian Cup final.

On 24 May 2021, he received his first call-up to the senior team for friendly matches against Croatia and Sweden.

[4] He made his debut on 1 June in a 1–1 draw against Croatia.

This biographical article relating to Armenian association football is a stub.