The decision is being seen as the latest move in a campaign by the authorities in Moscow to silence dissent and bar critics of Vladimir Putin from running for parliament in September.
The ruling prevents people associated with Mr Navalny’s anti-corruption foundation from seeking public office.
Foreign Secretary Mr Raab said: “Today’s ruling that the anti-corruption foundation FBK is an extremist organisation is perverse.
“It is another Kafka-esque attack on those standing up against corruption and for open societies, and is a deliberate attempt effectively outlaw genuine political opposition in Russia.”
Mr Navalny was arrested in January after recovering from a nerve agent poisoning that he blames on the Kremlin - a claim denied by Russia .
He was sentenced to two-and-a-half year prison term in February for violating the terms of a suspended sentence for an embezzlement conviction that he dismissed as politically motivated.