The arrests followed a 15,000-strong protest in the Nile Delta city of Tanta, where 23 of the arrests were made late Friday and early Saturday, said Ali Abd al-Fattah, a senior member of the Brotherhood. Five others were arrested in nearby Menoufia province, he added.
Police confirmed the arrests, and the number of protesters, but did not link the demonstration - thought to be the largest of late by Brotherhood supporters - with the detentions or give any reason for the crackdown.
An Egyptian legislator and member of the Brotherhood, Isam al-Aryyan, said none of the detainees had been charged.
"No on knows about the accusations leveled in such cases, as the arrest was just a punitive measure," al-Aryyan told Aljazeera on Saturday.
Abd al-Fattah said the group had not notified authorities ahead of time about the protest, as is customary, and claimed it had begun spontaneously and then grew fast.
''We didn't plan to hold a demonstration; it was only a conference on (political) reforms held inside the doctors' syndicate,'' he said. ''When the number of attendees increased, we had to leave the conference hall to the streets.''
Protesters raised small copies of holy Quran, waved banners and chanted slogans calling for comprehensive political reform, including an end to emergency laws, imposed after the 1981 assassination of President Anwar Sadat. They also demanded the abolition of laws limiting the formation of political parties.
The arrests late Friday and early Saturday bring to about 80 the number of Brotherhood members detained since a wave of arrests on 27 March, al-Aryyan said.
The Muslim Brotherhood has been banned since 1954, but remains Egypt's largest Islamic political group and is thought to be the most powerful opposition to the government, with tens of thousands of supporters nationwide.