Akhundzade joined the youth academy of Qarabağ at the age of 9, and worked his way up their youth categories.[2] He debuted with Qarabağ in a 4–0 Azerbaijan Premier League win over Shamakhi FK on 30 October 2022.[3] In his debut season, he helped them win the 2022–23 Azerbaijan Premier League.[4] On 22 February 2024, he scored the deciding goal in stoppage time after extra time to secure a 6–5 aggregate win over Braga in the Europa League knockout round play-offs, guaranteeing his team a place in the next stage of the competition.[5]