He had also played a key role in persuading Western governments to sanction Russian officials for human rights abuses and corruption.
The US state department has described Mr Kara-Murza as “yet another target of the Russian government’s escalating campaign of repression”.
Mr Kara-Murza, who comes from a Soviet dissident family, received British citizenship when he moved to the UK as a teenager with his mother.
His wife has expressed concern over his wellbeing while in prison, particularly following the death of opposition leader Alexei Navalny earlier this year.