Protesters raised a Romanian flag at the presidency entrance and a flag of the European Union atop the building, a RIA Novosti correspondent at the scene reported.
According to Moldovan daily Timpul, which cites eyewitnesses, protesters smashed several portraits of president Vladimir Voronin, whose term expires Tuesday.
Protesters also broke into the parliament building, from where they hurled furniture out into the street and set it ablaze.
About 30 people, both police officers and demonstrators, were injured and dozens of others required medical care, the head doctor of the Chisinau emergency hospital said.
Street protests come two days after a general election handed victory to the ruling communists of president Voronin.
Security forces have blocked entrances into Chisinau to stop other people from joining the protests and the Moldovan opposition called for a fresh election.