The violence broke out during a march of 5,500 Russian fans through the city ahead of tonight'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," spokeswoman Agnieszka Hamelusz said, when asked how many people had been arrested.
She said earlier that those held include Russians and Poles. It is not yet clear how many of them are Russians and how many are 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 center, where thousands gather to watch matches on a big screen.
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 told R-Sport that Polish fans had thrown pyrotechnics at the Russians.
Nikolai Komarov, a spokesman for the Russian Football Union, refused to comment when contacted by R-Sport, saying he was with the Russian team in their hotel in the city center.
The Russians were marching to celebrate Russia Day, a national holiday which commemorates the end of the Soviet Union.
The scuffles follow trouble on Friday when 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.
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