Amateur footage following Russia's 4-1 win in their Group A opener against Czech Republic has appeared online which shows dozens of supporters attacking a handful of officials in a main walkway inside the 40,000-capacity arena, which is home to Polish club side Slask Wroclaw.
Local police confirmed that the violence was caused by Russian-speaking supporters.
Police spokesman Mariusz Sokolowski 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."
When asked why the police did not step in to assist the stadium staff at the time, Sokolowski said: "It was at the stadium. We react when security and steward at the stadium cannot handle things. In this case they fast took control at the situation."
According to Eurosport's Polish office, four members of stadium staff were taken to hospital but all were 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 dissipates and he is helped to his feet, while another is kicked in the head while trying to evade a lone attacker.
Sokolowski added: "Nothing serious happened to the man who was kicked."
Russia's next match is against co-hosts Poland in Warsaw on Tuesday. According to reports, mayor Hanna Gronkiewicz-Waltz will decide whether or not to let the anticipated thousands of Russian fans travel to the capital for the game.
Eyewitnesses in the Ukrainian city of Lviv have also reported an incident involving Russian fans scuffling briefly with locals in the early hours of Saturday morning.
Around 15 Russian fans left the city's fan zone and started shouting and swearing at a smaller group of Ukrainians, said Reuters photographer Marian Striltsiv.
The two sides exchanged a few punches before local police quickly moved in and separated the combatants. No arrests were made.
One picture taken by a local agency showed a man with blood streaming from his nose.
Police denied there had been any violence and said they had prevented the two sides from fighting. Tensions between the two nationalities are particularly high in Lviv, in the far west of the country, in part because of Ukrainian resentment at Soviet rule from 1939 to 1991.
The Lviv region was the centre of a resistance campaign by Ukrainian nationalists fighting for independence from the Soviet Union during and after World War Two.
One of the main nationalist leaders was Stepan Bandera, a man still widely regarded as a hero in western Ukraine and as a bandit by Russia. Fans of local side Karpaty Lviv always show a huge banner of Bandera during home games.
Polish sports minister Joanna Mucha confirmed in a press conference that there were 16 reports of violent incidents and 314 people treated by medical staff in incidents connected to Euro 2012, meaning those which happened in either stadiums or fan zones.