"It's against the background of the local elections."
Hamdi Ibrahim, head of the group's branch in northern Cairo, was also arrested, along with three other senior members, the Brotherhood said.
The arrests took place during separate raids on homes of Brotherhood members and on a house north of Cairo where leaders within the group were meeting with Brotherhood candidates expected to stand in the local elections, a security official and the group said.
Ghuzlan, who spent eight months in custody without charges last year, is the first member of the Guidance Office to be detained since the current police campaign against the group began in mid-February.
The Brotherhood, Egypt's largest Islamic opposition movement, is banned as a political party but its members hold one fifth of the seats in parliament.
Two other members of the group's Guidance Office, including Kairat el-Shatir, the third-in-command, are in detention facing military trial, the group said.
On Wednesday, the Muslim Brotherhood vowed to contest the elections from their jail cells.
The group said the police campaign was timed to coincide with a 10-day registration period for candidates wishing to take part in the elections.
Thursday's arrests come on top of more than 350 others they have been picked up in the campaign, a Brotherhood spokesman said.
Egyptian security sources said only 25 had been arrested and said they were accused of belonging to a banned group and holding secret meetings.
Egypt postponed local council elections for two years in 2006 after the Brotherhood performed better than expected in a parliamentary election in 2005.
The local councils where seats are at stake in the April 8 vote hold little real power, but seats could be important nationally if the Brotherhood wants to qualify to field an independent candidate for the presidency in the future.