The move came after Foreign Minister Sergei Lavrov branded the action by the French police "an absolutely unacceptable incident".
The ministry said it summoned French ambassador Jean-Maurice Ripert over the detention of the Russian fans who were travelling from Marseille to Lille, particularly the "discriminatory and indiscriminate measures against Russian citizens".
Police had surrounded a bus carrying the fans at a hotel near Marseille and took them into custody over the clashes that erupted before and during Russia's match against England on Saturday.
"Further stoking of anti-Russian sentiments surrounding the topic of the participation of our squad in the Euro football championships could significantly aggravate the atmosphere in Russian-French relations," it said.