The Hobart-born 19-year-old hit a raised 'sausage' kerb at Parabolica and his Campos Racing car was flung high into the air before flipping and landing upside down on the tyre wall, coming to rest against the wire fence.
Peroni walked to the medical vehicle unaided. No other driver was involved, with the race finishing behind the safety car.
Formula One's final practice session before qualifying was delayed while repairs were made to the barriers and the offending kerb was removed.
Formula Three qualifying had to be halted on Friday for safety reasons after a queue of cars lined up on the back straight preparing to start their timed runs while others approached at speed.
A statement was later posted on Peroni's Facebook page confirming that the teenager was "in hospital and doing well."
The statement added that he was recovering from a fractured vertebra and concussion.
Safety in the support series to Formula One is under increased scrutiny after the events of Spa-Francorchamps last Saturday.
Hubert, 22, died after his car was hit at speed by Juan Manuel Correa's after the French driver had gone off into the barriers at Spa's fast Raidillon corner.
American-Ecuadorian Correa is on life support and in an induced coma in a London hospital.
Hubert was the first driver fatality at a Formula One race weekend since Ayrton Senna and Roland Ratzenberger were killed at Imola in 1994.