The MENA news agency said police detained son Abdullah Morsi, a 20-year old university freshman, after a police patrol found a suspicious car parked on the side of the road in el-Obour city, east of Cairo. Officers found two rolled hashish cigarettes in the car, the agency said.
Investigating police officer Lt Col Hazem Saad told the agency that Morsi's son confessed to possession of the hashish said to be around 5 grams.
A security official, speaking on condition of anonymity because he was not authorised to speak to reporters, said the car's passengers were Morsi's son and a friend.
"This is an attempt to smear our image," Osama Morsi, a lawyer, told to The Associated Press. "Half the members of this government consume alcohol and they are now accusing Morsi's son of consuming a substance that alters consciousness."
Morsi was toppled in a popularly backed military overthrow in July and has been in detention since, facing four separate trials.
His family so far has stayed out of legal trouble amid an intensive government crackdown on Morsi supporters and leading members of his group, the Muslim Brotherhood.