Karadzic, 63, was arrested by Serbian security forces last week after more than a decade in hiding. He will be tried at the International Tribunal for the Former Yugoslavia for his role in the 1992-95 Bosnia war, including the massacre of 8,000 Bosnian Muslims at Srebrenica in 1995 and the siege of Sarajevo, during which 10,000 people died.
He is being held at the Scheveningen detention centre outside The Hague, a short drive from the court where he is to be tried.
Around 16,000 Serb nationalists, who consider Karadzic a national hero, held a mass rally in central Belgrade on Tuesday night, organized by the Radical Party with the support of the Democratic Party of Serbia, led by former prime minister Vojislav Kostunica.
Protestors accused Serbia's pro-Western President Boris Tadic and his government of betraying the country's interests in extraditing Karadzic.
The protests gradually turned violent. Nationalists hurled rocks, Molotov cocktails, garbage and firecrackers at riot police, and 46 people, including 25 officers, were injured. Several shop windows were smashed during the violence.
The long-awaited arrest and extradition has been received by the European Union as a key step toward Serbia's accession to the 27-nation bloc.
The Serbian Justice Ministry issued a statement saying the decision to extradite Karadzic "was taken on the basis of the law on cooperation between Serbia, Montenegro, and the International Tribunal for the Former Yugoslavia."
Karadzic's lawyer, Svetozar Vujacic, said last week that Karadzic would defend himself at the UN tribunal in The Hague.
At the Scheveningen jail, where former Serb leader Slobodan Milosevic spent several years during his trial, Karadzic joins dozens of other war crimes suspects from the Balkan wars. Detainees are reportedly held in comfortable conditions, in roomy cells with satellite TV channels and access to a library and sports facilities.
