The rock slide happened at 2.30 am on Friday. The 38-year-old woman who was in the hut at the time was hit by falling stone as she went to investigate the noise.
Her husband, a shepherd, and two children aged two and four were with her in the hut, which received little damage.
The 20 minuti newspaper reported that the woman was carrying a baby when she was struck. The baby was unhurt.
The paper said a huge chunk of cliff had broken off the side of the Alp Lago sending around 10,000 cubic metres of rock down into the valley.
A group of 13 children attending a nearby summer camp organized by the environmental organisation WWF escaped with a fright.
The children aged from 10 to 13 and four adults with them were unhurt although their tents were erected close to where the rock came down.
“Luckily nothing happened to the children, but we are all very shocked,” WWF spokesman Fredi Lüthin told the Blick newspaper.
“The WWF has been running the camp in Val Cama for years, and we knew the family well.”
The campers had to be evacuated to nearby Grono.
The Rega rescue service and helicopters from Heli Rezia flew everyone down from the Alp del Lago into the valley below on Friday morning.
There a care team was waiting to help.
The Alp del Lago can only be reached by foot or air.
The hiking path to Val Cama has been closed on safety grounds as there is a risk of further rock fall.