The son of Muslim Brotherhood senior leader Khairat El-Shater was arrested in the early hours of Wednesday in northeast Cairo, judicial sources said.
Saad, 23, was rounded up in the Nasr City district on allegations of inciting violence, as part of a large-scale crackdown on the Islamist movement.
His father, El-Shater, a wealthy businessman widely seen as the Brotherhood's leading political strategist, is being detained on charges including inciting violence against anti-Brotherhood protesters.
The 85-year-old Muslim Brotherhood, which had operated in the shadows until the fall of autocrat Hosni Mubarak in 2011, has been reeling from a broad clampdown on its upper echelon and partisans following the army's overthrow of Islamist president Mohamed Morsi last month after mass protests against his rule.
Mohamed Badie, the group's top authority and spiritual leader, was arrested almost a week ago, marking the first time in three decades that the group's supreme guide is arrested.
Badie, along with his two deputies El-Shater and Rashad Bayoumi, are due to stand trial on 29 October after the first hearing was adjourned on Sunday because the defendants could not attend for security reasons.