Muhammad Abd al-Sattar, an engineer from the Fayum region, was detained by state security forces on 12 September, three days after his younger brother was locked up for handing out the leaflets.
Abd al-Sattar's corpse was returned to his family on 14 September. The police gave no explanation for his death, the Egyptian Human Rights Organisation said in a statement.
His brother remains in detention even though he has yet to be charged.
Torture is a crime punishable in Egypt by a sentence of up to 15 years in prison.
Last week, twelve police officers were ordered to stand trial at a criminal court in the city of Alexandria for torture, intimidation, fraud and attempted rape.