Following scattered fighting in the Polish capital before the match, police fired rubber bullets at a group of fans who attacked them with bottles and stones near an outdoor fan zone in central Warsaw where about 75,000 people were watching the game on huge screens. The game ended in a 1-1 tie.
None of the injured, which included a police officer, were in life-threatening condition.
About 5,000 Russian fans marched to the match at the National Stadium to celebrate the Russia Day national holiday. It was seen as provocative to many Poles. The two countries share a difficult history, including decades of control by Moscow over Poland during the Cold War. Many Poles felt authorities shouldn't have allowed the Russians to march as a group in Warsaw given the historical wounds.
One of the most violent incidents occurred during the march. Polish hooligans attacked 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. Poland and Russia fans were also seen fighting and throwing stones outside the stadium.
Following those incidents, the website of Moscow radio station Ekho Moskvy reported that Russian authorities were sending Mikhail Fedotov, head of the presidential council on human rights, to Warsaw to help deal with the situation.
Later, during the match, new fighting apparently unrelated to nationalist tensions broke out among Polish fans near the fan zone. Police responded with rubber bullets and tear gas and made some arrests. Some of the men wore Polish team T-shirts and one said he was attacking police simply because he didn't like them.
Before the game, Russian 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.
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 centre 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 were about to go 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."
Associated Press writers Vanessa Gera in Warsaw and Jim Heintz in Moscow contributed to this report.