Egypt's state-run Al-Ahram newspaper said a witness alleged it was court workers who set the tents on fire.
MENA, the state-run news agency, said the building had sustained serious damage and court employees reported being harassed by the demonstrators.
Protesters closed off Tahrir Square with metal barricades early Wednesday after a massive demonstration against the acquittal of former government officials.
Tens of thousands of protesters filled the square Tuesday, denouncing the acquittal of six former police commanders in the deaths of protesters last year. Protesters also called for the removal of Ahmed Shafiq from the presidential ballot, BikyaMasr.com reported.
Egyptian health officials said seven people were treated on-site Tuesday for injuries received during the protest and seven others were taken to a nearby hospital. Most of the cases involved fainting, though two people were injured by a sharp object.
A number of women protesting in the square Tuesday said they were subjected to sexual harassment, prompting a Facebook initiative to stop the assaults, BikyaMasr.com said.
The "Securing the Square" initiative calls for volunteers to monitor the square and report any attacks against women. Another initiative, HarrassMap, allows women to report their stories online.