A senior member of the group was reportedly among those arrested, it said.
The Brotherhood said the crackdown was aimed at preventing the group's members from running in municipal elections on April 8.
Hundreds of Brotherhood members have been arrested, and thousands of candidates from the group prevented from registering for the upcoming contests.
Although the Brotherhood is banned, its candidates run in elections as independents.
The group scored surprise victories in 2005 parliament elections that gave it a fifth of the legislature's 454 seats.
The upcoming local elections had been scheduled to take place in 2006, but were put off for two years, apparently out of fear of more Brotherhood gains.
Amnesty International criticised the government on Friday for its crackdown against the Brotherhood ahead of the municipal elections.
"Amnesty International is concerned that many of those arrested and detained may be prisoners of conscience held for the legitimate exercise of freedom of expression and association," the rights group said in a statement.
"Amnesty is calling for those who are being held as prisoners of conscience to be released immediately and unconditionally, and for the Egyptian authorities to lift all other unlawful restrictions on the exercise of freedom of expression."
Traditionally dominated by the ruling National Democratic Party, the municipal polls are expected to draw fierce competition after a constitutional amendment was passed in 2005.
Friday's arrests came two days before Egyptian textile workers and pro-democracy activists have planned a day of strikes and protests.
The Brotherhood has said that it supports the workers' right to strike but played no part in organising the protests. The group said it would not rally its supporters to join the strike because it felt the goals were unclear.
Labour organisers have called on thousands of textile workers to walk out of factories in the northern Nile Delta industrial city of Mahalla el-Kobra on Sunday to voice their dissatisfaction over low wages.
The city has already been the scene of a string of unprecedented strikes over the past year.
The pro-democracy group Kifaya, which in Arabic means "enough", has said it will hold a solidarity rally in Cairo's twin city of Giza.
Abdel-Halim Qandil, Kifaya's leader, said the move would support the workers and "express the grievances of the people ... in a day of anger".