Mehmed Alagic is led away for trial
The three, named as former generals Mehmed Alagic and Enver Hadzihasanovic, and a serving brigadier, Amir Kubura, are due to be flown out of Sarajevo airport after being arrested on Thursday at the tribunal's request.
Their detention prompted a call from the Muslim member of Bosnia's collective presidency for the Bosnian Serb authorities to hand over war crimes suspects still at large.
The tribunal's two most-wanted suspects - Bosnian Serbs Radovan Karadzic and Ratko Mladic - are both believed to be in hiding on Bosnian Serb territory.
Beriz Belkic's challenge came amid similar calls from the United States, Germany and Britain.
Mr Belkic - one of three members of the collective Bosnian presidency - said that, now the three Muslim army officers had been detained, the Serbs had been set an example.
"I appreciate that the authorities of the Muslim-Croat federation acted in accordance with The Hague's request," Mr Belkic told a news conference.
"I hope that the Republika Srpska authorities will start acting in the same way."
Charges
The indictment against them says the most serious charges they face are for crimes allegedly committed by foreign "mujahideen" fighters under their command. Hundreds of foreign troops went to Bosnia to join the army during the conflict.
The three officers were accused over "murders, inhumane treatment causing great suffering, wanton destruction and illegal detention", said tribunal spokesman Jim Landale.
Bosnian Muslim commentators say that some war crimes were committed by the majority Muslim Bosnian army during the war.
But they say that these were isolated incidents and not the planned genocide of which they have accused the Bosnian Serb and Bosnian Croat armies.
The Bosnian Government agreed to hand over the three men, having consistently promised full co-operation with the tribunal.
The parliament in the Serb Republic within Bosnia recently approved the first draft of a law on co-operation, but the authorities there have yet to arrest any of the indictees believed to be living on their territory.
All three Muslim officers accused have already appeared at The Hague tribunal, at the trial of Bosnian Serb General Radislav Krstic.
He was jailed for 46 years on Thursday for his role in the 1995 murder of almost 8,000 Muslim men and boys in Srebrenica, Europe's worst atrocity since World War II.
It was the court's first conviction for genocide - the most serious of war crimes - in connection with the Bosnia war, and the toughest sentence it has passed so far.