Nkunda, who has led a Tutsi rebellion in Congo's east since 2004 and is wanted for war crimes, was detained late on Thursday and Congo's government said it would seek his extradition.
Congolese and Rwandan military commanders said Nkunda was arrested after he tried to resist a joint Congolese-Rwandan operation launched this week to hunt Rwandan Hutu FDLR militiamen operating in Congo.
Nkunda's arrest has been widely viewed as being part of an agreement that allowed Rwanda to send over 3,500 troops into Congo this week, marking unprecedented cooperation between the Great Lakes neighbors after years of suspicion and hostility.
Aid workers said hundreds of children recruited to the rebel ranks might soon be free to leave as a result of the arrest.
Wars, rebellions and ethnic violence since 1998 have killed more than 5 million Congolese, holding back the development of the huge former Belgian colony in central Africa, which is rich in minerals such as copper, cobalt, coltan, gold and uranium.
"Ex-general Laurent Nkunda was arrested on Thursday, January 22 at 2230 hours while he was fleeing on Rwandan territory after he had resisted our troops at Bunagana with three battalions," Congolese and Rwandan military commanders said in a statement.
But an Nkunda associate said the founder of the Tutsi rebel National Congress for the Defence of the People (CNDP) had been "called for consultations" in Rwanda before he was arrested.
Diplomats and analysts said the arrest of Nkunda, coupled with the joint offensive against the Rwandan Hutu rebel FDLR (Democratic Forces for the Liberation of Rwanda), would help to bolster confidence between Congo and Rwanda. They have accused each other in the past of supporting hostile armed groups.
"It's pretty obvious by now that this is part of the deal between Kigali and Kinshasa to tackle both the FDLR and CNDP at the same time," independent Congo analyst Jason Stearns said.
Congolese Information Minister Lambert Mende said Congo would seek Nkunda's extradition for trial. "He is Congolese. He committed his crimes in Congo," Mende said.
Nkunda's leadership of his CNDP rebel group had been challenged this year by dissident rebel commanders who last week ended hostilities with the Congolese government.
"The CNDP's future is uncertain," Stearns told Reuters.
Human rights groups said they would be watching how Rwanda and Congo dealt with Nkunda. His fighters are accused of mass killings and rapes, and recruitment of child soldiers.
International Criminal Court prosecutors have a war crimes arrest warrant for Bosco Ntaganda, Nkunda's military chief who broke with him recently and is backing the Congolese-Rwandan operation against the FDLR. But a spokeswoman for the ICC Prosecutor declined to say if Nkunda would be prosecuted.
Many ordinary Congolese welcomed his arrest. "He must be brought back to Congo and face justice for his acts," said local Congolese pastor Crispin Kombozi.
UK-based charity Save the Children said Nkunda's arrest could mean the release of up to 1,500 child soldiers.
"There is no way of predicting what will happen over the next couple of days, but Nkunda's arrest is a real turning point and one we hope will lead to the escape or release of more child soldiers," country director Gilbert Hascoet said in a statement.
The Hutu FDLR presence in Congo has been a root cause of 15 years of regional violence. Some of their 6,000 fighters took part in Rwanda's 1994 genocide and they have been often pursued by Congolese and Rwandan Tutsi-led forces in Congo's east.
"Nkunda's scalp was a prerequisite, politically, for the joint operations about to get under way," Philippe de Pontet, analyst at the Eurasia Group, said in a note.
Late last year, Nkunda, who said his rebels were fighting to defend Congo's Tutsi minority against the FDLR, led his CNDP guerrillas in a big anti-government offensive in North Kivu.
The United Nations, which has 17,000-strong peacekeeping force in Congo, fears civilians could suffer in fresh fighting.