The violence broke out during a march of 5,500 Russian fans through the city ahead of Tuesday night's Euro 2012 match between the two nations at Warsaw's National Stadium.
Police fired warning shots into the air after coming under attack from Polish fans, some of whom had intercepted the Russian column.
"It's more than 100 hooligans," said police spokeswoman Agnieszka Hamelusz, when asked how many people had been arrested.
She said that those held include Russians and Poles. It was not clear how many were Russians and how many were Polish, she said.
Ten people were injured, including seven Poles, two Russians and a German, a statement on the Warsaw police website said.
Some of those arrested were held after an incident near the fanzone in the city centre, where thousands gather to watch matches on a big screen.
The police spokeswoman refused to comment when asked whether the disorder at the fanzone was connected to the march, how many people had been arrested, and whether the incident had finished.
Video courtesy: NDTV
Warning shots were fired during the march when Polish fans hurled bottles, stones and flares at police, who also deployed a water cannon.
At least one Polish fan was arrested after infiltrating the Russian parade and shouting inflammatory slogans.
Alexander Shprygin, head of the All-Russian Fans' Union, was with the Russian fans and said that Polish fans had thrown pyrotechnics at the Russians.
Nikolai Komarov, a spokesman for the Russian Football Union, refused to comment, saying he was with the Russian team in their hotel in the city centre.
The Russians were marching to celebrate Russia Day, a national holiday which commemorates the end of the Soviet Union.
On Friday, some Russian fans assaulted Polish stewards after Russia's 4-1 win over the Czech Republic in Wroclaw.
There was widespread anger in the Polish media after that match because some Russians displayed Soviet flags, seen by many in Poland as a symbol of foreign occupation.