Karimov has a career high ATP singles ranking of 426 achieved on 27 August 2018.

On 15 April 2019, he peaked at world number 279 in the ATP doubles rankings.

Karimov has represented Uzbekistan in Davis Cup, where he has a win–loss record of 4–1.

He achieved his first victory in 2018 against British player Cameron Norrie after coming from two sets down.

This biographical article relating to Uzbekistani tennis is a stub.