German police said they apprehended the 31-year-old suspect upon his arrival from Moscow.
The suspect was not named. Police said his victim suffered fractured bones and injuries to the brain and lungs.
He faces up to 15 years in jail in France for attempted homicide and grievous bodily harm.
German police only identified the victim as a 51-year-old England fan.
But Andrew Bache, from Portsmouth, was 51 when he was attacked during the tournament two years ago.
He suffered severe brain injuries and had to be placed in an induced coma, from which he has since emerged.
German federal police said the Russian suspect was identified following a joint investigation with British police over the course of almost a year and a half.
Police said the suspect had been the subject of an international arrest warrant issued by French authorities late last year.
He was arrested during a flight change at Munich airport, while on his way to Bilbao in Spain for a Europa League game.
"It seems he didn't count on the good co-operation of European law enforcement agencies," the police statement said.
"Now he's sitting in jail in Munich."
The police officer credited with helping to save Mr Bache's life in 2016 said people had described the scene as being similar to a zombie film.
PC Stuart Dickerson saw "about 150 Russian hooligans who were clearly trained in fighting", wearing boxing gloves and gum-shields, and carrying metal bars and other weapons.
"It was like a load of locusts going through a cornfield," the English officer - on deployment in France - said.
"They were just randomly assaulting any England fan that was in their path."
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