The raid took place at the Umma Studies Centre in the Manyal quarter of the Egyptian capital, where Muslim Brotherhood figures from five provinces had been meeting.
The group's lawyer said the men detained were "from the political section of Brotherhood".
The Egyptian interior ministry said the people arrested were attending "a secret organisational meeting of Brotherhood cadres".
Police took publications, documents and computers from the centre, the statement said.
The prosecutor general has ordered that the men be held for questioning for 15 days, judicial sources said.
Egyptian authorities have begun a new crackdown on the group, calling it a "secret organisation", despite the presence of 88 of its members in the 454-seat lower house of parliament.
The Brotherhood's website said: "This escalation comes against the background of the widespread detentions among the Brotherhood by the security forces during the Egyptian uprising to support the judges in their position towards the government."
The Brotherhood helped to organise street protests in May in solidarity with two judges who faced disciplinary proceedings for speaking about allegations of vote-rigging last year.
Police organised plainclothes security men to attack the demonstrators and dozens were detained.