In a statement, the Qalioubiya Security Directorate said Abdullah Morsi and A. A, an employee, were arrested in a car in Obour, a commercial residential district in eastern Cairo
According to the statement, the pair were arrested in possession of two hashish (marijuana) cigarettes and were referred to prosecutors for investigation.
But the family of the ousted president described the arrest as an attempt to "tarnish the image of honorable people".
"The charges aim to tarnish the reputation of the sons of the president," Abdullah's brother, Osama, told Anadolu Agency over the phone.
He argued that the family had received warnings about attempts to fabricate charges against Morsi's sons.
Osama and his elder brother Ahmed have been banned by Egypt's military-backed authorities from travelling abroad. No reasons have been given for the move.
By Hussein Qabani
englishnews@aa.com.tr