According to Metro UK, villagers in Northiam, near Rye, East Sussex, said the man turned up at his ex-partner’s home before opening fire at about 4pm.
Armed officers who went to the scene amid reports the gunman was at large found a man’s body in a car parked outside.
Sussex Police said the girl – described to be of primary school age – is in a life-threatening condition with a gunshot wound in King’s College Hospital, London.
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.
‘We are treating this as an isolated incident and there is no evidence that any other members of the public are at risk