Alyokhina, 24, is serving a two-year sentence for a protest performance against President Vladimir Putin's rule at Moscow's main Russian Orthodox Cathedral.
Prison authorities at the penal colony in Perm, in the Urals, said Alyokhina asked to be moved to a single-person cell because of tensions with fellow inmates.
Alyokhina and two other members of the punk-activist collective were convicted in August of hooliganism motivated by religious hatred for their anti-Putin performance.
In court, they stressed that theirs was a political protest and not directed at religious faith, although they acknowledged cozy relations between the Kremlin and Orthodox Church elite were among their concerns.
Supporters said their trial was part of a crackdown on dissent.
Nadezhda Tolokonnikova, 23, is serving her two-year sentence in a penal colony in Mordovia.
Yekaterina Samutsevich, 30, was freed last month after an appeals court suspended her sentence.