The prefecture in France's Savoie region said the fatal avalanche occurred Sunday at the Val-d'Isere ski resort, close to the Italian border.
Local newspaper Le Dauphine said on its website that the two victims were a 44-year-old man and his 11-year-old daughter from the Paris region.
Le Dauphine reported the two were skiing on a run that was closed due to the avalanche risk.
Swiss media initially reported that 10 people were buried by the other avalanche, in the southern canton (state) of Valais.
But Valais police spokesman Stefan Leger says only two people pulled from the snow Sunday were hospitalized.