The newspaper Novaya Gazeta Europe said Kara-Murza had written to his lawyer Maria Eismont that the move was punishment for not standing up at the right time, which he said the authorities had deemed a "malicious violation".
Kara-Murza said he had been sent to a type of punishment cell known by its Russian initials as an EPKT, the strictest form of isolation from other inmates.
The newspaper quoted him as commenting ironically that the point of the punishment was "so that life doesn't seem like honey".
Kara-Murza, who had lobbied for Western sanctions against Russia, was sentenced to 25 years last April on treason and other charges that he denied, comparing the case against him to a Stalinist show trial.
His wife said on Monday that he had been moved from his previous prison in Omsk and his whereabouts were unknown.
(Writing by Felix Light and Mark Trevelyan; Editing by Kevin Liffey)
