The security services said last week they had arrested 33 members of Hasan al-Turabi's Popular Congress for plotting sabotage with help from Sudan's eastern neighbour Eritrea.
"Shams al-din Idriss ... died from brain damage and his hand and also his leg was broken ... he was tortured." al-Turabi's secretary, Awad Babikir said.
The Interior Ministry said it had no information on the case of the 25-year-old.
Earlier, the ministry said it had discovered an arms cache north of the capital Khartoum in a dawn raid on Friday, including 100 machine guns and 10 mortars. Sudan's media carried photos of the weapons.
The UN says more than a million
Darfurians have been displaced
The weapons were hidden by a member of the Popular Congress in collaboration with three others, said the ministry.
Al-Turabi is under house arrest, accused of inciting tribal tensions.
The government has accused al-Turabi's party of involvement in a rebellion in the vast western Darfur region - scene of what the United Nations calls the world's worst humanitarian crisis.
The party denies the charge.
One Popular Congress official said the number of arrests was increasing and had reached about 60.
Babikir said a policeman had gone to Idriss's family home and told the father the death had occurred on Saturday because of stomach problems.
But when the family took the body to a doctor he found the "reason of death was brain injury and (that) he also had a broken hand and leg", said Babiker.
The United States said on Thursday the Darfur conflict amounted to genocide and blamed the government and militias known as Janjawid for the violence.
The United Nations estimates about 50,000 people have been killed, more than one million have been displaced and that 200,000 refugees are in neighbouring Chad.