Czech defender Theodor Gebre Selassie was the victim of monkey chants during Friday night's Group A game in Wroclaw, while fans were caught on camera attacking stewards in a walkway at the Municipal Stadium.
A statement on the Russian FA website read: "We appeal to all fans who are in Poland. Remember that you represent your country. Respect yourself, your home and your team."
Russia, who beat the Czechs 4-1, take on co-hosts Poland in their next match in Warsaw on Tuesday and trouble is expected.
Violence erupted at the Russia-Czech Republic game when a handful of stewards were attacked by large group of fans inside the 40,000-capacity ground.
Footage of the incident has emerged online and police spokesman Mariusz Sokolowski was reported by Eurosport to have said: "I can confirm that this happened at the stadium.
"The attackers were from the group of Russian language fans. We are trying to identify them.
"Police have the security footage from the stadium. We are looking into it."
Reports claimed four members of stadium staff were taken to hospital and released later that evening.
The footage shows one steward left in a heap on the ground after being set upon by several assailants before the violence dissipated and he is helped to his feet, while another is kicked in the head while trying to evade a lone attacker.