"The government helicopters came to protect the Janjaweed (Arab militias) who were attacking civilians in our areas and our troops shot down one of them," said rebel Sudan Liberation Army (SLA) leader Minni Arcua Minnawi.
He said the incident happened six or seven km (four or five miles) east of Shearia town in South Darfur state, where displaced people had fled after recent fighting in the town. The SLA had intervened to protect them, he added.
"All the other crew are dead. Only he (Captain Zubeir) survived," he told Reuters.
A Sudanese army spokesman confirmed the news of the helicopter, which he said was downed by rebels using artillery in the Jabel Reel area near Shearia.
He said an officer was injured in the crash but could not confirm his name or if he had been captured by the rebels.
A tentative truce was signed between the two main rebel groups and the government in April 2004, but has since been violated many times.
The ceasefire specifies Khartoum can fly helicopters in the vast region the size of France but not on offensive missions.
Tens of thousands of people have been killed and more than 2 million forced from their homes during three years of conflict in Darfur, violence Washington has called genocide.
Khartoum denies the charge but the International Criminal Court is investigating war crimes accusations in the western Sudanese desert region.