No replacement for Nour was immediately announced.
Former members of the United Front for Democratic Change (FUC), which Nour once led, come from the Tama ethnic group and have been resisting efforts by the army and Deby's own Zaghawa ethnic clan to disarm them.
Chadian troops and ex-FUC fighters clashed on Friday at Guereda, an eastern border town in the Tama heartland.
Deby himself had been directing combat operations this week against fighters from another rebel group, the Union of Forces for Democracy and Development (UFDD), which abandoned a month-old peace accord a week ago.
The president's sacking of his defence minister injects further uncertainty into the situation in the conflict-torn east of the country.
It comes ahead of the planned deployment there of a European Union peacekeeping force early next year.
The EU force has been tasked by the United Nations to protect refugees and aid workers.
On Friday, the UFDD declared a "state of war" against French and foreign military forces in an apparent warning to the peacekeeping force.
The UFDD is led by Mahamat Nouri, another former defence minister, who defected to join a two-year-old eastern campaign against Deby.
Diplomats said Nour's sacking could trigger more bloodletting around Guereda between the Tama and Zaghawa clans.
Chad declared a state of emergency last month along its eastern border with Sudan after ethnic fighting between the Tamas and Zaghawas killed at least 20 people.
Meanwhile, Deby celebrated the 17th anniversary of his assumption of power following his coup against predecessor Hussein Hebri.
A military parade was staged on Saturday to commemorate the occasion.