Pyotr Verzilov, who ran on to the pitch during the FIFA World Cup final, reportedly fell ill after a court hearing on Tuesday and was taken to hospital in a serious condition, the BBC reported on Sunday.
His symptoms allegedly included losing his sight and ability to speak.
His flight to Germany was reportedly organised by the Cinema for Peace Foundation.
A fellow Pussy Riot member, his former wife Nadya Tolokonnikova, is said to have welcomed him at the airport.
A short video and photographs that appear to show him on the plane, then being transported on a stretcher, were shared by German tabloid Bild.
Verzilov was one of four members of the group to invade the pitch, dressed in a police officer's uniform, during the World Cup final between France and Croatia on July 15.
It was part of a protest against Russian police brutality after a series of torture allegations were reported from prisons and police interrogation rooms across the country, the Guardian said.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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