Aisoltan Nijazova, internationally wanted by Turkmenistan, has after the arrest been transferred to the Polish police.
She will be taken to the prosecutor's office, probably on Monday, and then a court will decide on the next step, says police spokesperson Tomasz Krupa to AFP.
Nijazova, who has Turkmen origins, was arrested after crossing the border from Lithuania. She has previously been arrested in Slovenia and Croatia after an international arrest warrant, but then quickly released again.
Pussy Riot are frequent critics of Russia's president Vladimir Putin and opponents of the Russian war of aggression in Ukraine.