The two girls were sleeping with a third sister, who was slightly bruised, and their parents, who were unhurt, at the Camping Verde Mare in Marina di Massa.
The town is in the Versilia seaside region, around 120 kilometres north-west of Florence.
The family, from the Turin area, was vacationing there.
The younger victim was declared dead on site, while the older one passed away in hospital.
The tree – a 4.5-metre poplar – fell during a violent thunderstorm, amid a weekend bout of severe bad weather in large parts of northern Italy.
Similarly in Varese province, some 100 kilometres north-west of Milan, a man was reported missing after falling in a river, while in Tuscany firefighters rescued a woman who fell in the Ombrone river.