The video, posted on YouTube by a Polish user, showed a large crowd of Russian fans fighting with stewards.
One member of the security team was wrestled to the ground and repeatedly kicked by the group of men, including one who was shirtless.
Another security guard attempted to intervene, but he was punched by the same shirtless man, then kicked repeatedly in the head -- martial-arts style -- by a younger fan.
Around 20 or 30 fans were involved in the incident, and order was restored in less than minute, enabling Czech fans to leave the stadium.
"Russians freak out at Euro 2012 in Wroclaw...Judge for yourself," wrote the author of the video, which could not be independently verified. "Stewards abused and no one responded ... what will happen in Warsaw?"
In a separate incident, Russian fans celebrating the 4-1 win in the Ukrainian city of Lviv clashed with local fans. The fighting lasted for about a minute before police pulled the groups apart, the Interfax news agency reported.
Russia plays Poland in Warsaw on Tuesday.