The avalanche occurred soon after midday at around 2,500 metres above sea level, just below the Pic de la Font Sancte.
The woman, who was hiking in a group of 20 at the time, had already gone into cardiac arrest by the time emergency services arrived, reported Le Dauphine newspaper.
Despite the efforts of paramedics on hand, the woman died at the scene.
Two other people were swept up in the snow but managed to survive. Both were taken to a hospital in Briancon. The other hikers managed to avoid the avalanche.
The avalanche risk in the area at the time was three out of a possible five.
Local authorities have launched an investigation into the death, with police warning other hikers and skiers to be vigilant while in the Alps.
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Avalanches in the French Alps have proved deadly several times this year, with six soldiers killed while training in mid-January, just days after a separate avalanche killed two children when a school group went off piste.