The incident happened at the Armancette glacier near Mont Blanc in south-eastern France around midday on Sunday local time.
It’s thought the victims were among a group of hikers.
According to BBC, Mr. Darmanin said several others were injured and a search and rescue operation was underway.
Officials from the Haute-Savoie prefecture, the local authority in charge of the area, put the number of injured at nine.
Both he and French President Emmanuel Macron expressed their sympathy to the victims and their loved ones.
Before the incident, the nearby ski resort of Contamines-Montjoie posted a video on social media showing a huge wall of snow moving down from the Dômes de Miage, which the glacier is a part of.
The resort urged people to be careful if they were venturing off-piste – away from the prepared ski runs.
Officials have told the AFP news agency that a further avalanche could not be ruled out.
Two brothers died in an avalanche on the same glacier in 2014.
They were both experienced mountaineers and had been properly equipped.
