The search was interrupted overnight for safety reasons, police in the southwestern Swiss canton of Valais said, and rescuers indicated that hopes of finding her alive faded after several hours of digging and probing on Saturday.
Two helicopters with a guide and specialists flew to the high mountain slope near the village of Bourg St Pierre early Sunday, but efforts to secure the site for a renewed search failed, police said in a statement.
Fresh avalanches added a weighty layer of snow totalling 20 metres (65 feet) in places, hampering any digging and adding to the risks for search parties.
"For this reason and to guarantee the safety of rescuers, the search was interrupted," the statement added.
Patrick Torrent of the Air Glaciers rescue service told Swiss radio RSR earlier that the assessment would be based on the weather, "the remaining dangers on site and an evaluation of the chances of survival with the doctor."
The party of 11 high altitude hikers from nearby France equipped with skis or snowshoes was caught in the avalanche on Saturday.
Five of them were injured and flown to hospitals in the towns of Martigny and Sion, police said. Three were in a serious condition, police said Sunday.
Ten helicopters and more than 20 rescuers with tracker dogs were mobilised in an emergency search-and-rescue operation after the alarm was raised at around 12:30 pm (1030 GMT) on Sunday by one of the group who escaped unscathed.
All the victims were French nationals, police said. The dead included two women aged 57 and 65 and a 64-year-old man. But another woman who died in hospital as well as the missing hiker have yet to be formally identified.
Rescuers failed to detect a signal to localise her swiftly under heavy, packed, wet and suffocating snow.
"Even with only one or two legs caught, one person on their own without a spade could not have pulled themselves out of this type of snow," Torrent said.
Police said conditions would be reviewed regularly to see if a search could resume.
The team came from a mountaineering club in Cluses, at the foot of the Alps in nearby eastern France, a French mountaineering official said, and were equipped with avalanche detectors.
"These are very experienced people," Georges Elziere, president of the French Federation of Alpine Clubs, told AFP. "They know the mountains perfectly well, they are not at all beginners."
It was the worst toll in an avalanche in Switzerland this winter, according to a count by the Swiss news agency ATS.