Jacques Desillets said the suspects were accused of attacking a vehicle taking the money to a bank in Goma, the main city in eastern DR Congo.
Two people were killed and another two were wounded in the robbery, he said.
There was a mass escape from a jail in Goma when it was under rebel control last month, Mr Desillets added.
Nearly 1,000 prisoners were still at large, he said.
Mr Desillets, the deputy police commissioner for the UN peacekeeping force in DR Congo known as Monusco, told the BBC’s Focus on Africa programme that Congolese police had asked their Rwandan counterparts to extradite the suspects.
He did not have further details about their discussions, he said.
‘Walked to Rwanda’
Mr Desillets said the robbery took place in “broad daylight” on Tuesday, when gunmen opened fire on a vehicle transporting the money from the airport on the outskirts of Goma to a bank in the city.
The driver was killed, along with “someone else sitting at his desk right near” the road after being hit by a stray bullet, he added.
Two other people in the vehicle were wounded, Mr Desillets said.
He said that after stealing the money, the robbers had sped off in their own vehicle towards the Rwandan border.
“Just before they arrived at the border, they dropped off the vehicle and just walked across to Rwanda with the money,” Mr Desillets added.
“The information we have received today [Wednesday] is that the Rwandan authorities would have intercepted the three suspects, presumably would have recovered the money and communication is going on between Congolese and Rwandese police as far as extradition is concerned.”
The M23 rebel group, made up of deserters from the army, captured Goma from government and UN troops last month.
It later withdrew from the city, following widespread international condemnation and pressure from the Rwandan and Ugandan governments.
The UN and DR Congo government accuse Rwanda and Uganda of backing the rebels, an allegation they strongly deny.
Mr Desilletts said he did not know who the robbers were.
“There is a lot of criminal activity going on, unfortunately…. Monusco is doing everything they can [to restore order],” he added.