The country's Interior Ministry said the arrests for "various offenses" at Sunday's game between CSKA Moscow and Lokomotiv Moscow came five days after President Vladimir Putin signed legislation aimed at decreasing violence at sporting events into law, RIA Novosti reported Monday.
The Fan Law, aimed at keeping hooligans from raising havoc at the 2018 FIFA World Cup in Russia, officially takes effect in January.
Meanwhile, the Europol European law enforcement agency said it is looking into alleged soccer match fixing by Russian organized crime groups.
The agency said an organized Asian crime syndicate was discovered to have been fixing soccer matches around the world in February.
"This problem isn't one just linked to Asian organized crime. We also have our suspicions about Russian mafia groups involved in match fixing. We are looking at that for the moment. Also we are looking at some organized crime groups originating from the western Balkans," agency chief Rob Wainwright said.