The popular Islamist organisation said Saad Sayyid Muhammad Qutb, 43, died on Monday at the headquarters of the Egyptian state security forces in Cairo.
"He underwent several sessions of interrogation and different kinds of torture," a statement said.
Senior Brotherhood official Sayyid Tarili said "this crime exceeds the red lines ... and we will in no case accept this blood-letting and these criminal practices".
The police were not immediately available for comment.
'Monstrous and unacceptable'
The Brotherhood's supreme guide, Maamun al-Hodaibi, said the death was "monstrous and unacceptable".
"We will file a complaint and demand that the authorities launch an investigation. This must not happen again," he warned.
He added the Brotherhood had "several times in the past warned the authorities against cases of torture" of its members.
The Egyptian Human Rights Organisation said the death occurred after he was admitted to Umm al-Misriyine hospital "where he died without having received medical care".
"We will file a complaint and demand that the authorities launch an investigation. This must not happen again"
It said that the "hospital report mentioned several injuries on the body" and urged the authorities "to take the necessary steps to stop the practice of torture".
Speaking later on, al-Hodaibi said the continuing arrests and torture cases have "disappointed the hopes" pinned by the Brotherhood on recent pledges made by President Husni Mubarak's regime to reform.
He said the dialogue underway between Mubarak's National Democratic Party and several opposition groups was "worthless and useless" because it excludes the Brotherhood.
The group has a "sweeping popularity in all sections of society", he added in a speech in the Cairo Sheraton hotel.
Al-Hodaibi renewed his organisation's commitment to "dialogue" and its call for the regime to "undertake reforms in all fields" and to abolish the emergency laws imposed on Egypt almost without a break since 1967.
The laws grant authorities extensive powers to detain people deemed a threat to national security for 45-day renewable periods without charges.
Al-Hodaibi ended his speech with a tribute to the jailed members of the Brotherhood and prayed to God that they are "released safe and victorious".
He also urged their families, many of whom attended the banquet, to be patient.
The Brotherhood, which was created in 1928 by the Egyptian Hassan al-Banna and spread to other Arab countries, calls for the establishment of an Islamic state by peaceful means.
"The (Egyptian)government intensified its crackdown on suspected political opponents, tightened its control over civil society institutions, and clamped down on freedom of speech and expression"
Human Rights Watch report 2003
The movement is represented by 16 deputies in the 454-member parliament, making it the main opposition force in Egypt.
They were elected in November 2000 as independents because of the ban on much of the Brotherhood's activities.
Although Brotherhood members are frequently arrested on charges of trying to revive a banned organisation, they are active in professional associations and universities as well as in mosques.
Appalling rights record
In its 2003 report on Egypt, Human Rights Watch condemned the country's appalling human rights record.
It said the government intensified its crackdown on suspected political opponents, tightened its control over civil society institutions, and clamped down on freedom of speech and expression.
Thousands of political suspects remained in prolonged detention without trial under emergency legislation, and there were a series of grossly unfair trials before military or state security courts.
Human Rights Watch added that torture and ill-treatment of political detainees remains common.