Those arrested included a businessman and senior local leaders of the group in Behira, located about 180 km north of Cairo, according to a statement posted on the Brotherhood's website.
Amendments
The arrests were the first since the referendum on controversial constitutional amendments, which the Brotherhood and other Egyptian opposition groups boycotted.
The amendments, the largest since the constitution was drafted in 1971, carried new restrictions on civil liberties and was seen as aiming at deterring the Brotherhood from being recognised as a legal political player.
Authorities initially intensified their campaign against the Brotherhood after student members of the group staged a militia-style demonstration at Al-Azhar University in Cairo in December, stoking government fears the group was forming a military wing.
The group denied this, saying the new campaign was a reaction to their opposition to the constitutional amendments.
The movement, banned since 1954, is Egypt's largest Islamic opposition group. Its members of parliament, who run as independents, currently hold 88 seats in the 454-seat parliament.