Anti-riot police used tear gas and rubber bullets to disperse around 100 hooligans pelting officers with stones near a Belgrade ultranationalist rally in support of Mr Karadzic.
At least two policemen were seen being helped into an ambulance, but it appeared their injuries were not serious.
After almost half an hour of skirmishes between the police and hooligans, the rioters dispersed, with many protestors fleeing the tear gas.
The 63-year-old is appealing his extradition to the Hague where he faces charges of genocide, war crimes and crimes against humanity before the International Criminal Tribunal for the former Yugoslavia.
He was arrested in Belgrade eight days ago after more than a decade on the run.
Mr Karadzic's lawyer said he was confident a ploy to delay his client's transfer to the Hague had worked.
The only confirmation the appeal was filed came from Mr Karadzic's brother Luka, who said it had been sent from a remote post office at the very last minute permitted under Serbian law, just before a midnight deadline.
Once the appeal is received, a three-judge panel of the Serbian court has three days to decide on its merits before the justice ministry must issue a final order for the transfer of Mr Karadzic to the ICTY in The Hague.
Ultra-nationalists have staged daily protests in support of Mr Karadzic since his capture, some of them marred by attacks on journalists and threatening chants against Serbia's pro-Western leaders.
Hospital footage
Meanwhile, Serbian state television RTS has shown footage of Mr Karadzic, under his alter ego of alternative health guru Dragan Dabic, attending a celebration at a private hospital on 22 June.
'Good afternoon, how do you do,' Mr Karadzic, with a long grey beard and grey hair tucked under a white hat, was heard saying.
His eyes hidden behind the thick glasses, Mr Karadzic presented his female companion to his host, a doctor called Sava Bojovic.
His voice and accent appeared different from his last public appearances back in 1996.
Mr Karadzic vanished from public life in that year, shortly after the ICTY issued an arrest warrant for him.
Whilst in hiding, he completely changed his appearance and identity, styling himself as Dabic and donning the large glasses and white Panama atop long white hair and a bushy beard.
Mr Karadzic's brother Luka visited the ex-Bosnian Serb leader in a detention cell in Belgrade again yesterday, bringing him two suits, local media reported.
Further details about the operation that snared him also emerged, with police sources quoted in the daily Press saying more than 50 secret service agents had tracked Mr Karadzic for months after acting on a tip-off.
Serbian Interior Minister Ivica Dacic said a search of Mr Karadzic's last hideout in his Belgrade flat had uncovered military documents of his Bosnian Serb regime.
The documents concerned meetings of his military chiefs of staff from Republika Srpska, the self-declared state Mr Karadzic carved out during Bosnia's 1992-1995 war. An entity of the same name exists in post-war Bosnia.
Such documents were likely to be used at Mr Karadzic's trial in The Hague, since Serbia is obliged to provide the ICTY with its archives for court proceedings.
Mr Karadzic is notably accused of playing a leading role in the 44-month siege of Sarajevo, which claimed more than 10,000 lives, and the Srebrenica massacre of 8,000 Muslim males - the bloodiest atrocity in Europe since World War II.
His arrest - greeted with celebration in Sarajevo - improved the prospects of Serbia joining the EU, which has set Belgrade's cooperation with the ICTY as a precondition for membership talks.
However it has caused a spike in nationalist sentiment in Serbia, where the opposition is trying to pile pressure on the new pro-European government, accusing it of treachery.
