Police fired tear gas as at least 100,000 protesters approached the palace. The crowds pushed aside a barbed wire barricade that is several hundred yards from the palace.
Morsi was reportedly left through a back door when the crowds got bigger.
After police fired tear gas, they abandoned the rest of the barricades, choosing not to try and push the crowds back. There were no attempts to storm the palace yet.
Eighteen people were injured in the outburst of violence, but there were no reports of casualties.
Many in the crowd were chanting "erhal, erhal," Arabic for "leave, leave" and "the people want to topple the regime" - two well-known chants from the 2010-2011 Arab Spring revolts that toppled Mubarak and other Middle Eastern and North African rulers.
The protest follows a quickly adopted draft constitution by Morsi's allies that gives him sweeping powers. The president has called for a referendum on the draft constitution next week.
The Associated Press contributed to this report.
