Ndaw and Ouane had been heading the interim government with the declared aim of restoring full civilian rule within 18 months. Former president Ibrahim Boubacar Keita was ousted in a military coup last August.
On Tuesday, the two men were arrested and taken to a military establishment at Kati, 15 kilometres from the capital.
Their "resignation" was confirmed by a spokesman for one of the arresting officers, Assimi Goita. Goita, who is a serving colonel and holds the post of vice president in the transitional government, led the coup against Keita. He accuses Ndaw and Ouane of failing to consult him on a government reshuffle which was announced on Monday.
A mediation team from regional bloc Ecowas, led by Nigerian former president Goodluck Jonathan, has held discussions with Goita.
In a statement read on national television on Tuesday, Goita said Ndaw and Ouane had been stripped of their duties for seeking to "sabotage" the transition, which would, he said, "proceed as normally".
"The scheduled elections will be held in 2022," he said.
International condemnation
Monday's cabinet reshuffle, designed to respond to growing criticism of the interim government, saw the military keep the strategic portfolios it controlled in the previous administration.
But two coup leaders -- ex-defence minister Sadio Camara and ex-security minister Colonel Modibo Kone -- were replaced.
"This kind of step testifies to the clear desire of the transitional president and prime minister to seek to breach the transitional charter," he said, describing this as a "demonstrable intent to sabotage the transition," Goita said in reaction to the reshuffle.
The transitional charter, a document largely drawn up by the colonels, sets down principles intended to ensure Mali's return to civilian rule.
The UN Security Council is to hold an emergency meeting later Wednesday at the request of former colonial power France and others.
The detention of Ndaw and Ouane sparked international condemnation, including a rare joint statement by the United Nations, the African Union, the Economic Community of West African States, the European Union and the United States.
French President Emmanuel Macron has condemned the arrest of the interim leaders, describing it as "a coup within a coup".
