Many luxury shops and banks had their windows smashed or covered in graffiti with messages like: "Rich people are ugly" and "Fuck this society".
The facade of Geneva's main theatre, the 19th century Grand Théâtre, and the sculptures lining its entrance were splashed with black and coloured paint, interspersed with white graffiti.
"The damage is considerable," Geneva police spokesman Jean Philippe Brandt told AFP.
The wildcat demonstration was organized on social media to protest against budget cuts for alternative culture sites, even as Geneva "is subsidizing the Grand Théâtre, a bourgeois culture site with prices out of reach for most people."
The demonstration began around 10pm outside the central train station, Brandt said.
Some 400 people showed up, but a hard-core group of around 30 people were responsible for most of the damage, he said.
Police had blocked off parts of the city to try to halt their movement, but had not immediately made any arrests.
"It is difficult to do so in the heat of the moment. Now we are investigating to try to clarify who the main culprits were," Brandt said.
On Sunday morning, Geneva residents appeared shocked by the damage, with many stopping to take pictures as work began to scrub clean the Grand Théâtre facade.
The head of Geneva's security ministry, Pierre Maudet, meanwhile told the Tribune de Genève daily he was "furious and scandalized by this intolerable vandalization."
"We are dealing with a gang of professional hooligans," he said, calling for the perpetrators to be "severely punished."