A march by thousands of Russian fans to mark their national day had to be halted and some missiles were thrown.
Police say 56 arrests were made and that seven people were injured in the violence.
Tensions are running high, given the centuries of rivalry between the two countries.
About 6,000 police were on duty to keep the rival fans apart.
The match began at 20:45 local time.
Beforehand, some Polish fans on a bridge on the march route had tried to attack the Russian fans and had been involved in scuffles.
It was relatively easy for police to contain clashes while the Russians fans were heading down a planned route, but it may more difficult when they spread across town later.
Tear gas, rubber bullets and water cannon were used to disperse fans at the end of the march, according to Poland’s state news agency.
In a separate incident, 50 Polish fans in masks attacked Russian fans in a Warsaw cafe, the Russian news agency Interfax reported.
Russia occupied Poland for more than a century and dominated it during the Cold War, after World War II.
The conservative Polish opposition condemned the march as a provocation, but it was approved by the authorities.
The Russian national holiday marks Russia’s declaration of sovereignty in 1990 – a key episode in the demise of the Soviet Union.
Polish media highlighted fears that some Russian fans may sport Soviet flags and symbols – a highly sensitive issue for the many Poles who deplored communist rule.
“March or street war?” said a headline in the conservative Polish daily Rzeczpospolita. It quoted Wojciech Wisniewski, a member of the Polish Union of Football Fans, as saying “somebody really wants to make Polish football fans attack the Russians”.
European football’s governing body UEFA has opened disciplinary proceedings against Russia after a series of incidents involving the country’s fans at Euro 2012.
Russian fans were caught on camera kicking and punching stewards inside the stadium at Wroclaw, in western Poland, after their team beat the Czech Republic 4-1 on Friday. Four stewards needed hospital treatment.
Anti-racist monitors at the match said a section of the crowd racially abused the Czech Republic’s only black player, Theodor Gebre Selassie.
In a statement on Monday, Russian football association said: “We urge all football fans now in Poland to remember that they represent Russia. Please respect yourselves, your country and your team.”
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