Ahmed Gadhaf al-Dam later surrendered, but faces charges including possession of weapons and ammunitions and attacking the police, al-Masry al-Youm reported Sunday.
Gadhaf al-Dam is not an Egyptian citizen and does not have the right to political asylum in the country, Samir Girgis, the head of international cooperation at the prosecutor general's office, has said.
The Libyan was coordinator of Egypt-Libya relations during the regime of the late Moammar Gadhafi, and Girgis said Gadhaf al-Dam would be extradited if Libyan officials clarified certain issues raised by prosecutors.
Gadhaf al-Dam can be held in prison for 30 days before he is released, the Egyptian newspaper said.
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