The accident happened in the Vinschgau, a part of the German-speaking province of South Tyrol in Italy.
The 45-year-old woman and her daughter were part of a nine-person ski group.
An accident report of the National Emergency Call Centre shows that the avalanche occurred at the 8,406-feet high Seekoepfl Mountain at an altitude of around 6,890 feet above sea level.
According to local media, the skiers probably triggered the avalanche themselves just off the official slopes of the Haideralm ski area.
The bad weather conditions on Wednesday made the rescue mission very difficult.
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Because of the strong northerly wind, a rescue mission by helicopter was initially not possible.
The dispatchers therefore sent a rapid response team with special blankets to the scene of the accident.
According a spokesman of the Bolzano Police, the 11-year-old child and her mother were dug out of the snow mass by the rescuers.
Unfortunately, the schoolgirl died from her injuries at the scene.
The seriously hurt mother was taken to a hospital in Silandro, where she died of her injuries later in the evening.
The victims have been identified as German tourists from the city of Ludwigsburg in the South-Western state of Baden-Wuerttemberg.
The other seven skiers who were part of the group were not hit by the avalanche.
Authorities in South Tyrol have warned of an increased avalanche risk in the Alps.
This week, an avalanche also killed a skier near Kandersteg in the Canton of Bern, Switzerland.
In Grisons near the Oberalp Pass, a German couple were hit by an avalanche, but survived their ordeal.