The MB-339 jet had exploded moments after takeoff at around noon local time, officials said, according to the Italian Fire Brigade.
The pilot, who survived, could be seen ejecting with his parachute opening moments before the jet struck the ground, the fire brigade said.
He is currently being treated for burns at Giovanni Bosco Hospital in Turin, officials added.
The Frecce Tricolori aerobatic jets, part of the Italian Air Force, were practicing a formation ahead of the 100-year celebrations of the Italian Air Force that are set to take place Sunday. The planes had just taken off from Turin’s Caselle airport when one of the jets started to lose altitude, as seen on multiple videos that were shared on social media.
The crash happened inside the airport perimeter.
The airport tweeted that it was closed temporarily.
Italian media reported that the jets hit a flock of birds just after takeoff, according to CNN affiliate Sky24.
The car which held the five-year-old child and her family had been driving along a country road parallel to the airport, according to local media reports.
Her brother survived and is now being treated for severe burns at the Regina Margherita Children’s Hospital in Turin, the hospital confirmed.
Their parents have also reportedly suffered burns.
The Italian Air Force said it was “dismayed and astonished” by the jet crash, according to a statement made by the Italian Chief of Staff of the Air Force and Air Squadron General Luca Goretti.
The Pony 4 aircraft, piloted by Major Oscar Del Do’, had lost altitude and crashed to the ground shortly after the formation had taken off, the statement said.
The Italian Air Force has not confirmed the exact cause of the accident, but has hypothesized there was a bird strike during the very first phases of takeoff.