The 51 members of the 2nd Foreign Engineer Regiment of the French Foreign Legion were backcountry skiing when the incident caught the group by surprise, according to police.
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He added four more people were injured and another two hypothermic.
They were among about 50 soldiers participating in off-piste maneuvers, away from prepared skiing tracks, near the Valfrejus ski resort in the French Alps town of Savoie when the avalanche struck.
He said the slopes were closed after the avalanche on Monday for safety reasons.
The avalanche took place at an altitude of between 2,350 and 2,600 metres.
It is believed they had been training at a centre for mountain warfare in Modane, near the border with Italy.
The incident comes just days after three people, including two students, were killed when a school group in the Alps was swept away by an avalanche.
The risk of avalanches in the Alps has been high in recent days after heavy snow falls were followed by strong winds, leading to unstable formations of snow high up in the mountains.
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All the soldiers taking part in the exercises were carrying an avalanche detection system and rescuers were on the scene within minutes, reports said.
