“We will not rest until Kosovo is again under Serbia’s control. Hitler could not take it away from us, and neither will today’s Western powers.”
Protesters broke into the US compound and briefly set part of the embassy alight. The UK, Belgian, Croatian and Turkish missions were also attacked.
The violence followed a peaceful rally earlier by at least 150,000 people outside the main parliament building.
The US, UK, Germany and Italy are among those to have recognised Kosovo.
The BBC’s Nick Hawton in Belgrade says smoke and tear gas are drifting across the main square, where Prime Minister Vojislav Kostunica earlier delivered an impassioned speech condemning the territory’s secession.
Most Serbs regard Kosovo as their religious and cultural heartland.
One protester climbed onto the first floor and ripped the US flag from its pole. Riot police backed by armoured cars fired tear gas at the protesters.
Several other embassies were also attacked by angry crowds. There are reports of various businesses and restaurants being attacked and flames billowing from some of the premises.
Correspondents say ambulances have been travelling across Belgrade and there are reports of up to 100 people having been injured.
Serbia, supported by Russia and China, says Kosovo’s Sunday declaration violates international law.
Mr Kostunica addressed the crowds from a large stage, saying: “As long as we live, Kosovo is Serbia. Kosovo belongs to the Serbian people.”
“We’ll never give up Kosovo, never!” the crowd responded.