Mary Shipstone was seven and lived in Spring Hill, Northiam, with her mother and brother.
Trained police officers and hospital staff are currently supporting the family through their terrible ordeal.
Mary was shot shortly before 4pm on Thursday outside her home by a man in a car parked on a driveway next to her home. She was taken to King's College Hospital in London but sadly died at 2.56pm today
The seven-year-old girl, believed to have been shot in the head by her father, has died in hospital.
Sussex police have named the little girl as Mary Shipstone.
Her father Yasser Alromisse, appears to have killed himself.
He turned up at his ex-partner's house in Spring Hill, Northiam, near Rye, East Sussex, at about 4pm yesterday before opening fire from a car parked on a driveway next to her home.
The seven-year-old girl, shot in the head, was a pupil at Beckley Church of England Primary School in Rye.
The school has issued the following statement: "We have received confirmation that the child who was shot is a pupil at our school.
"This is a dreadfully sad and shocking incident and the whole school community are praying for her and her family."
Video from the scene of the shooting at Northiam in Sussex. A schoolgirl was seriously injured. A man's body was found nearby.
The schoolgirl, shot in Sussex, is still in hospital in a critical condition. A man's body was found in a car nearby. An area around Spring Hill in Northiam was sealed off yesterday. Police say they're not looking for anyone else.
Chief Supt Neil Honnor, of Sussex Police, said that "we probably need to prepare ourselves for bad news" in relation to the young girl's condition.
He told BBC Radio Sussex: "She's still alive, but gravely, gravely ill and our hopes are with her but in many ways we probably need to prepare ourselves for bad news.
"She's in the care of experts but is very, very unwell."
He declined to comment on reports that the man had turned the gun on himself but said it was a "hypothesis that we are working with".
And he said the shooting was believed to have been connected to the girl, describing it as a "domestic" related incident.
Explaining how the events unfolded, he went on: "As the officers got there, a young girl of six years old had been shot and was gravely ill.
"Some distance away but in Northiam in the Spring Hill area we then found a vehicle that we believe was involved in the shooting.
"We had to secure the vehicle with the containment and that was where members of the public were asked to stay inside their homes while we ensured the area was safe.
"Some short time after we managed to secure entry to that vehicle and found a man inside who was deceased and we were able to secure the area."
The area was still a crime scene with some cordons in place as officers sought to "unpick" the circumstances that led up to the shooting.
Efforts were under way to explain to children at the girl's school's what had happened, Mr Honnor added.
A 6yo girl believed to have been shot by her dad remains "gravely ill" and "we probably need to prepare ourselves for bad news", police say
A neighbour of a young girl who was shot in the head said the whole village "went into lockdown" shortly after the gunshot was fired.
Anthony Burr described "the panic" that swept across the Northiam to Good Morning Britain.
"We got all the kids in, locked all the doors, shut the gates and went into lockdown making sure everyone was safe in the vicinity."
A girl of "primary school age" shot in East Sussex today is in a "life-threatening condition" in hospital, police said.
Chief Superintendent Neil Honnor, Sussex Police's divisional commander for East Sussex, said:
We are treating this as a tragic domestic incident and do not believe that anyone else is involved.
At this stage we are not in a position to confirm the relationships of all those involved but we can say that the girl and the man knew each other. The man does not live at the address.
We are treating this as an isolated incident and there is no evidence that any other members of the public are at risk.
A resident of an East Sussex village where two people were shot today said he believed those involved were members of the same family.
A young girl is in hospital after it is believed she was shot in the head by her father who has been found dead, sources said.
One villager, Anthony Burr, said: "What appears to have transpired is that a father has gone to his ex's house where his daughter lives and has shot her. This has all come from neighbours and eyewitnesses."