He made his first team debut on 6 March 2011 in the Kazakhstan Premier League match against Irtysh, at the age of 18, and since then was a member of the Taraz's first-team squad.

[1] Islamkhan has earned the Kazakhstan Football Federation's Young Player of the Year award as voted on by the coaches for his performances in his campaign for Taraz during the 2012 season.

On 4 July 2013, he made his debut in the UEFA Europa League, coming on as a substitute in the 62nd minute in a first qualifying round match against Botev Plovdiv.

[12] During 2014 FIFA World Cup qualification tournament, Islamkhan played two times coming on as a substitute in matches against Sweden and Austria.

[13][14] In November 2022, after completing a two-year suspension, Bauyrzhan Islamkhan received a call-up to the Kazakhstan national team for friendly matches against Uzbekistan and the UAE.