Minchev made his professional debut with Levski Sofia during the 2014–15 season of Bulgarian Basketball League and played in 5 games.

[3] On 13 February 2017, Minchev was loaned to a Serbian club Vršac for the rest of the 2016–17 season.

[4] On October 1, 2017, Minchev was loaned to Macedonian club MZT Skopje for the 2017–18 season.

[8] On July 18, 2021, Minchev signed with OSE Lions of the Hungarian Nemzeti Bajnokság I/A.

In 2017 he made his debut with the Bulgarian senior national team playing in the 2019 FIBA Basketball World Cup qualification.