An unknown assailant on a motorbike threw the bomb in front of the main entrance of the Al-Qubba palace before fleeing, the sources said.
There has been a wave of violence in Egypt since Islamist president Mohammed Morsi was toppled by the military in July 2013 and a crackdown was launched on his supporters, leaving more than 1,400 people dead.
Egyptian President Abdel Fattah al-Sisi, the man who toppled Morsi, is currently attending the World Economic Forum in Davos, Switzerland.