A military spokeswoman told AFP the assailants, believed to be Palestinians, threw a Molotov cocktail at the car near the Maale Shomron settlement.
The car caught fire and the 11-year-old girl was seriously wounded while her father was slightly hurt in the attack, the spokeswoman said.
Housing Minister Uri Ariel of the far right Jewish Home party called on the army to retaliate to firebombs as it does to attacks from the Gaza Strip.
The air force yesterday launched an air strike in southern Gaza and killed a Hamas militant after a sniper attack from the Palestinian territory seriously wounded a soldier.
Firebomb attacks by Palestinians against Israeli civilians and military targets are not rare in the West Bank.
According to the military, in the first nine days of December Palestinians carried out 24 Molotov cocktail attacks, five of them targeting civilian Israeli cars.
