Police said 10 people were injured; seven Poles, two Russians and one German.
In what appeared to be the most violent incident, Polish football hooligans were seen attacking Russians, who responded violently. The two sides, made up of dozens of men, kicked and beat each other in the face, while flares could be seen exploding in their midst.
Associated Press journalists saw several people lying injured and bleeding on the ground, with one of them appearing to be seriously hurt. Poland and Russia fans were also seen fighting and throwing stones outside the stadium.
There were a number of other incidents as well, which came as about 5,000 Russia fans waving their country's flag marched to the stadium in a show of patriotism seen as provocative to many Poles.
The march was considered a huge security challenge and police were bracing for possibly more trouble after the match.
The two countries share a difficult history, including decades of control by Moscow over Poland during the Cold War. Many Poles felt the Polish authorities should not have allowed the Russians to march as a group in Warsaw given the historical wounds.
Russia fans clashed with police on a bridge near the National Stadium and police were later seen making arrests.
The news agency PAP reported that police used water cannons and tear gas to quell the disturbances.
In another incident, a group of clearly drunken Polish men began fighting among themselves, hitting and kicking each other. Two were on the ground bleeding and police intervened, throwing two more to the ground. The men were holding cans of beer and mumbling and one appeared to be unconscious. An AP reporter witnessed the incident and saw police detain three people.
Police spokeswoman Monika Brodowska said 100 fans on both sides were involved in fights. She said 56 people have been detained and police are studying security camera footage as they try to identify others involved.
One Russian who didn't have tickets to the game, but made the two-day car trip from Moscow simply to be in be the city, said it was wrong for the Russians to march in Warsaw given the countries' troubled history.
"The march, it wasn't right. It was a provocation. It shouldn't happen like this. But there are also aggressive Poles and we are scared here," said the 26-year-old man, who gave only his first name, Petya.
He and a friend had hoped to cross a bridge leading from the city center to the stadium to soak up the atmosphere in the area. But they gave up that notion and were sitting outside, sipping on beers from a distance, and planning to watch the match on TV in an apartment with friends.
In recent days, Polish media have tried to stir up nationalistic sentiments over the match, suggesting the encounter would be more than a simple football competition. Newspapers Monday were full of dramatic references to Poland's victorious 1920 battle against the Bolshevik Army, known as the Miracle on the Vistula.
The Super Express tabloid carried a front page mocked-up picture of Poland coach Franciszek Smuda charging on horseback, saber in hand, in a 1920 Polish army uniform under the headline "Faith, Hope, Smuda" — a play on an old army motto: "Faith, Hope, Motherland."
