"Authorities searched the house at night and confiscated [Ghozlan's] personal computer, his son's personal laptop as well as documents," the group said on its website, describing the arrest as "another escalation by the government against Brotherhood members".
The latest arrests are part of a crackdown launched in December after students affiliated to the Islamist movement held a militia-style parade on the campus of al-Azhar university in Cairo.
The government accuses the group of seeking to revive its secret wing from the 1940s that carried out violent attacks.
But the Brotherhood says the crackdown is aimed at quelling dissent over a series of constitutional amendments proposed by Hosni Mubarak, Egypt's president.
Opposition parties and observers argue the amendments are aimed at bolstering Mubarak's ruling party and excluding the Muslim Brothers from future elections.
Despite being officially outlawed, the popular movement managed to secure a fifth of parliament, far more than any other opposition group, in 2005 polls marred by widespread reports of fraud and voter obstruction.