The 23-year-old was rushed to hospital and underwent emergency brain surgery after tumbling from the monument to Italian general Alfonso Ferrero La Marmora, in the centre of Piazza Bodoni, early on Wednesday morning.
The man sustained head injuries after falling several metres from the equestrian statue, which he is believed to have climbed as a dare or in order to take a selfie.
Local media reported that he remains in intensive care, in a stable but critical condition.
The man, who is reportedly the son of a manager for Italo-American car maker Fiat Chrysler Automobiles, had been drinking with friends before the accident, according to Italian daily La Repubblica.