Al-Zawahiri was arrested Saturday and the charges against him have not been confirmed, Ahram Online reported.
Sources said al-Zawahiri, the brother of al-Qaida leader Ayman al-Zawahiri, is being kept under tight security.
Earlier in August, Ayman al-Zawahiri accused the United States of plotting with Egypt's military to overthrow former President Mohamed Morsi.
The son of Mohamed al-Zawahiri, Abdel Rahman al-Zawahiri, criticized the arrest of his father, al-Masry al-Youm said.
He claimed that the Interior Ministry is arbitrarily arresting Islamists, and said that his father did not take part in any protests.