Last year, a cholera outbreak there killed 147 people.
Madut said the symptoms of the second disease were similar to yellow fever, but the patient died quickly. He appealed for medical experts to go to south Sudan to diagnose the disease and help stop its spread.
"Up to this time the death toll is over 1,000 this week alone," Madut's statement said.
"As I am writing this press release, I am expecting other death reports sooner or later."
The "meningitis belt" that stretches across Africa from Senegal to Ethiopia through some of the world's poorest countries, including Sudan, accounts for more than half of the cases of the disease that are reported worldwide each year.
Meningitis is an infection of the thin lining that surrounds the brain and spinal cord.
It can cause complications including brain damage and deafness. Between 5 per cent and 10 per cent of patients die from the illness, according to the World Health Organisation.
Hundreds of thousands of southern Sudanese have been heading back to the region after a January 2005 peace deal which gave it autonomy from the government in Khartoum.
The returning refugees are especially at risk because they live in crowded camps where infectious diseases thrive.