"I tendered my resignation today and pray to God Almighty to keep Egypt safe and spare us more bloodshed," Abdel-Aal said.
The resignation was submitted to Deputy Premier and Higher Education Minister Hossam Issa.
Egyptian security troops forcibly dispersed on Wednesday two major protest camps for Morsi supporters in Cairo's Rabaa al-Adawiya Square and Giza's Nahda Square.
Clashes flared between angry Morsi supporters and security forces in several provinces nationwide.
The Health Ministry said Thursday that at least 578 people had been killed in the violence, including 228 people in Rabaa and 90 people in Nahda.
The official death toll given by the Health Ministry remains far below figures given by the National Alliance for the Defense of Legitimacy, a coalition of pro-Morsi Islamist parties and figures, which has put the number of deaths from the dispersal of the Rabaa al-Adawiya sit-in alone at some 2,600.