There have been several other clashes in recent weeks in Mitrovica, which is controlled by Serbs in the north and Albanians in the south.
Kosovo, a southern Serb province, broke away in February 2008, but its police, justice and customs services are still overseen by the European Union.
The Serb minority in Kosovo does not recognise Pristina's declaration of independence, which has so far been acknowledged by 62 mostly Western nations.
Tensions between ethnic Albanians and the EU have also escalated in recent months, highlighted by a separate event on Tuesday when activists rallied against the bloc's presence in the region.
Kosovo police said they arrested 20 ethnic Albanians in Pristina after they attacked the mission's vehicles by hurling stones, slashing tyres and overturning cars.
Self-Determination, an organisation founded by youths, wants to see Kosovo gain full independence from Serbia and the international community.
The EU mission, knows as Eulex, said in a statement it "strongly condemns" the damage caused by activists and that such incidents would not further their cause.
"Whilst Eulex supports the idea of peaceful protest as an important element in any democratic society, committing criminal damage does not further the interests or the arguments of any such protesters," the statement said.
Eulex has around 2,000 staff on the ground in Kosovo, which also hosts almost 14,000 international troops serving under Nato's Kosovo Force and a small contingent of the United Nations.