It follows violence at the England-Russia Euro 2016 match in Marseille.
Alexander Shprygin was among 43 Russian fans detained on Tuesday while on their way to Lille to watch Russia's second fixture, against Slovakia.
More than 12 Russians who were arrested following the trouble have been released without further action.
Three other detained Russian fans have been given jail sentences of up to two years over the violence in Marseille.
Separately, Marseille prosecutor Brice Robin said he was investigating an attack on two England fans ahead of the 1-1 draw with Russia as attempted murder.
Six English fans have been given shorter jail sentences for the violence.
The Russian foreign ministry said the 20 fans would be placed on a flight from Nice to Moscow on Saturday.
The arrests have angered the Russian government, which summoned the French ambassador to protest.
Russian President Vladimir Putin on Friday called the fighting "a disgrace" but added that he did not "understand how 200 of our fans could beat up several thousand English fans".
He called on Russian fans to behave appropriately when they face Wales on Monday.
"I hope that there are sober-minded people among them who really love sport and understand that any violation is not supporting their favourite team but damaging to the team and to sport," Mr Putin said.
A group of 150 Russian hooligans were involved in the trouble on 11 June, according to French officials. They say they have viewed more than 200 hours of footage but were unable to identify all those responsible.
Mr Shprygin's All-Russia Supporters Union is backed by the Kremlin. He is reported to hold far-right views and has been photographed giving a Nazi salute.
Russia and England fans clashed before and after the two teams played last Saturday.
Afterwards, Russia was hit with a fine and a suspended disqualification, meaning the team will be thrown out of the Euro tournament if their fans cause more trouble inside stadiums.
Five England fans were jailed for throwing bottles at police and a sixth jailed in connection with the violence.
The far-right leader of the Russian football supporters' association is due to be deported from France later, along with 19 fellow fans.