The move on Monday came ahead of a referendum the organisation says would lead to sham elections.
The detention order is intended to allow time for further investigation into activities of the 25, arrested in Sunday dawn sweeps.
They are accused of belonging to an outlawed group and possessing and preparing to distribute leaflets urging Egyptians to boycott Wednesday's referendum.
Prosecutors' orders ensure Mahmoud Ezzat, number four in the Brotherhood hierarchy, and the 24 others will be behind bars while Egyptians decide whether to accept changes to the constitution that would allow for the country's first multi-candidate presidential election in September.
Protests have been held for
greater political reform
Ruling party seeks control
Mubarak, president for the past 24 years, has been regularly re-installed in yes-no referendums in which his name is the only one on the ballot. He has not formally announced he will run again but is widely expected to do so.
Government opponents, including the Muslim Brotherhood, say the new system is being set up to ensure President Hosni Mubarak's ruling National Democratic Party still controls the election outcome.
Protests demanding greater political reform, many of them led by the Muslim Brotherhood, have been staged in Cairo and around the country in recent months.
More than 800 other members of the popular and powerful organisation remain in custody as a result of this month's protests. Hundreds more have been arrested and released.
"The arrests, made by the government to terrify us, would not change the Muslim Brotherhood group's determination to continue demanding people's right to freedom"
Mohammed Mahdi Akif,
Mohammed Mahdi Akif, the supreme guide of the group, told Aljazeera on Sunday that the arrests were in response to the movement's determination to continue demanding freedom of citizens and respect of the constitution and the law.
"The arrests, made by the government to terrify us, would not change the Muslim Brotherhood group's determination to continue demanding people's right to freedom," he said.
The group, founded in 1928, has been banned since 1954 but tolerated.
Fifteen Brotherhood supporters sit as independents in parliament, the largest opposition bloc.
But Mubarak has vowed not to allow any religious-based parties to seek office.