Video shows the pilot, who survived, ejecting moments before impact followed by a huge fireball near Turin Airport.
The girl’s nine-year-old brother was seriously hurt, while their parents suffered burns, BBC reported.
Deputy Prime Minister Matteo Salvini said the crash was a “terrible tragedy”.
Video filmed near Turin’s main airport shows nine aircraft gaining altitude in two tight formations before one peels away and starts to fall out of the sky.
As the plane crashes to the ground, thick black smoke billows as the pilot can be seen parachuting after ejecting from the aircraft.
According to local Italian media, an initial investigation suggests the aircraft may have collided with a flock of birds, possibly causing an animal to enter the engine and leading to engine failure.
The jet was part of the Frecce Tricolori demonstration team which had been due to take part in an event marking 100 years of the Italian Air Force on Sunday.
This event has now been cancelled, according to Reuters.
Defence Minister Guido Crosetto added: “The ministry expresses its condolences to the family members.
He added officials “had made available every facility and skill for the handling of the emergency and in support of any people involved”.
Writing on social media, Mr Salvini confirmed the pilot “jumped out with his parachute at the last moment”.
“A frightening tragedy,” he added. “A prayer and a hug of touching closeness.”
MNA/PR
