It was not immediately clear whether the Brotherhood supporters holed up inside who had been battling the protesters late Sunday fled the building overnight.
Morsi's critics view the Brotherhood headquarters as the seat of real power in Egypt, consistently claiming that the Islamist group's spiritual leader, Mohammed Badie and his powerful deputy, Khairat el-Shater, were the ones actually calling the shots in the country, not the president.
The Brotherhood has in recent weeks fortified the building's walls in anticipation of the massive opposition protests in which millions took part on Sunday in a display of anger and frustration with the Islamist leader on the anniversary of his inauguration.
On Monday, anti-Morsi protesters were gearing up for a second day of demonstrations.
Some protesters spent the night in dozens of tents pitched in the capital's central Tahrir Square and in front of the president's Ittihadiya Palace. They have vowed to stay there until Morsi resigns. The president's supporters, meanwhile, continued their sit-in in front of a major mosque in another part of Cairo.
The anti-Morsi demonstrators are calling for widespread labor strikes in an attempt to ratchet up the pressure on the president, but it was not immediately clear whether unions would respond to the call. Organizers are also calling for sit-ins at the Cabinet building, interim parliament, and another presidential place where Morsi has been working since late last week.
Sunday's protests were the largest seen in Egypt in the 2½ years of turmoil since the ouster of autocrat Hosni Mubarak in February 2011.
Fears were widespread that the collisions between the two sides could grow more violent in coming days. Morsi made clear through a spokesman that he would not step down and his Islamist supporters vowed not to allow protesters to remove one of their own, brought to office in a vote deemed free and fair.