It says Khalil Ibrahim was killed in fighting in the Wad Banda area in North Kordofan.
The claim has not been independently verified.
Khalil Ibrahim is known as the leader of the Justice and Equality Movement in conflict-torn Darfur. Earlier this year, he returned from exile in Libya after the fall of Col Gaddafi’s regime.
Sudanese army spokesman Sawarmi Khaled Sa’d told the BBC Arabic Service that Mr Ibrahim was killed at dawn.
The spokesman also told Sudan’s state TV that Mr Khalil Ibrahim and other rebel leaders had been trying to enter South Sudan, which seceded from Sudan in July.
Khartoum had accused Jem of fighting for Col Gaddafi in his attempt to hold on to power.
Col Gaddafi’s fall in Tripoli was a blow to the rebels as he gave them sanctuary and financial and military aid, analysts say.
The rebels signed a ceasefire with the Sudanese government in February 2010 but abandoned peace talks soon after, accusing Khartoum’s forces of launching new raids in Darfur.
About 300,000 people have died in the conflict in Darfur since it began in 2003, the United Nations says.
