Serbia announced earlier on Tuesday that war crimes suspect Karadzic, who had been on the run for over a decade, had been arrested. The former president is expected to be extradited to stand trial at The Hague war crimes tribunal.
"We hope the investigation and the trial of Radovan Karadzic will be unbiased," the ministry said. "We are drawing attention to this issue as the International Criminal Tribunal for the Former Yugoslavia has many times demonstrated bias."
Russia criticized the tribunal for 'bias' in favor of ethnic Albanians in armed conflicts following the breakup of Yugoslavia. The acquittal earlier this month of Naser Oric, a former Bosnian Muslim commander, on charges of failing to prevent the murder and torture of Bosnian Serbs in 1992-1993 was condemned by Moscow as "biased."
Karadzic was accused by the UN tribunal of genocide over the 1995 Srebrenica massacre, the largest mass murder in Europe since the end of WWII, when about 8,000 Muslim men and boys were killed by Serb forces led by Ratko Mladic, who remains at large.
Karadzic was also held responsible for the deaths of 12,000 people during the almost four-year long siege of Sarajevo.
Crowds gathered on the streets of Sarajevo, now the capital of Bosnia and Herzegovina, to celebrate the news of Karadzic's arrest, which was also welcomed by Western states.
The Foreign Ministry also said The Hague tribunal should step up work to prepare for its closure and the handover over unfinished cases to authorities in countries formerly within Yugoslavia.
The tribunal, which has convicted 161 people for crimes committed during the breakup of Yugoslavia, is due to close down by 2010.
Earlier on Tuesday, the ministry said Serbia should decide for itself whether Karadzic is to face a UN tribunal.
"We consider this to be an internal affair for Serbia, whose authorities should make an independent decision on whether to hand Karadzic over to the International Criminal Tribunal for the Former Yugoslavia," the ministry said.
The arrest of Karadzic was one of the main conditions specified by the EU for granting Serbia membership.