Mitkov started his career in his local Spartak Varna, before moving to Ludogorets Razgrad.

[2] Mitkov made his professional debut for the first team on 14 August 2020 in a league match against Slavia Sofia.

[3] On 12 January 2021 he joined the fellow First League team CSKA 1948 on loan for the rest of the season.

[4] On 16 February 2023, Mitkov moved to Rubin Kazan in the Russian First League on loan until the end of the season.

[7] On 3 August 2024, Tajikistan Higher League club Istiklol announced the signing of Mitkov on a contract until the end of the 2024 season.