The 42-year-old Moscow-born Kara-Murza, who has Russian and UK passports, was jailed after repeatedly condemning Russia's war in Ukraine and calling for foreign sanctions against his country.
His wife said he was transferred on Thursday evening to the prison hospital in Omsk, where he is incarcerated, but gave no further details about his condition.
She said his lawyers had waited five hours to see him but were denied visitation rights.
Kara-Murza suffers from a nerve condition called polyneuropathy after surviving two poisoning attempts and has repeatedly voiced concerns about his health in prison, his wife said.
She has reiterated those concerns several times since February 16, when leading opposition figure Alexei Navalny died in an Arctic penal colony.
Kara-Murza's jail term, handed down in April 2023 after what he described as a show trial like those under Soviet dictator Josef Stalin in the 1930s, was the harshest such sentence since Russia's full-scale invasion of Ukraine in February 2022.
Kara-Murza was arrested in April 2022, accused of spreading false information about the armed forces and declared a "foreign agent".
Hours earlier, CNN had broadcast an interview in which he said Russia was run by "a regime of murderers".
A former journalist, he was later charged with treason over speeches he gave about the war, including one to the Arizona House of Representatives in March 2022 in which he said Russian President Vladimir Putin was bombing Ukrainian homes, hospitals and schools.
Russia says it does not deliberately target civilians although thousands have been killed in Ukraine.
Kara-Murza lost an appeal against his conviction in May, the month he won the Pulitzer Prize for commentary for columns which he wrote from prison and were published in the Washington Post.
