Morsi was in the Itihadiya presidential palace conducting business as usual Tuesday when the complex was surrounded by tens of thousands of protesters chanting slogans reminiscent of those used during the 2011 revolution that ousted former President Hosni Mubarak.
He left through the back gate, but a presidential official said he returned to work on Wednesday. The official spoke on condition of anonymity because he wasn't authorized to speak to the media.
Morsi, who narrowly won the presidency in a June election, his aides and visitors routinely use other gates.
The huge scale of the protests has dealt a blow to the legitimacy of the new charter, which Morsi's opponents contend allows religious authorities too much influence over legislation, threatens to restrict freedom of expression and opens the door to Islamist control over day-to-day life.
The country's powerful judges also have said they will not take on their customary role of overseeing the vote in protest.
Tuesday's protest was peaceful except for a brief outburst when police used tear gas to prevent demonstrators from removing a barricade topped with barbed wire and converging on the palace.
Soon after, with the president gone, the police abandoned their lines and the protesters surged ahead to reach the palace walls. But there were no attempts to storm the palace, guarded inside by the army's Republican Guard.
Protesters also commandeered two police vans, climbing atop the armored vehicles to jubilantly wave Egypt's red, white and black flag and chant against Morsi. The protesters later mingled freely with the black-clad riot police, as more and more people flocked to the area to join the demonstration.
The protesters covered most of the palace walls with anti-Morsi graffiti and waved giant banners carrying images of revolutionaries killed in earlier protests. "Down with the regime" and "No to Morsi," they wrote on the walls.
In Alexandria, some 10,000 opponents of Morsi gathered in the center of the country's second-largest metropolis, chanting slogans against the leader and his Islamic fundamentalist group, the Muslim Brotherhood. There were smaller protests in a string of other cities across much of the country.