Two of the men were arrested in Poland and three in Germany, the Russian news agency RIA Novosti reported.
The Local.de said the suspects are from Russia's volatile Chechen Republic, as were most of the 200 migrants they allegedly moved.
"The criminal group operated from various European countries and recruited Polish taxi drivers to transport the migrants across borders and to asylum centers in Germany," Europol said in a statement.
Investigators believe the group brought in 200 migrants in less than a year, charging them 1,500 euros ($2,000) each.
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