The fire broke out at around 01:30 (00:30 GMT) during new year celebrations in a bar called Le Constellation in Crans-Montana. BBC reported.
Officials investigating the incident have not confirmed any cause, but categorically ruled out an attack.
People from multiple countries have been affected. Regional police commander Frédéric Gisler said the priority in the coming days was to identify those who had died "so that their bodies can be returned rapidly" to their families.
Thirteen helicopters, 42 ambulances and 150 emergency responders were sent overnight to the scene of the fire in the Valais region, which is popular with tourists.
Most of the injured experienced severe burns and 60 people were sent to Sion hospital in Valais, with a "significant number" in a critical condition, Regional governor Mathias Reynard said.
Its intensive care unit was at full capacity and Reynard said the local community must take extra care to avoid needing hospital treatment unnecessarily.
"We are painfully aware that identifying the bodies, as well as the injured, may still take a terribly long time for the families involved," Reynard added.
Some people have been taken to hospitals in other Swiss cities including Lausanne and Zurich which have specialist burns units.
A spokesperson for Lausanne University Hospital said they were treating 22 patients with burn injuries, while Zurich University Hospital said it was treating 12 patients for burns.
Some patients were transferred to Geneva University Hospitals where they were being treated for severe, "third degree" burns, and were "very young... between 15 and 25 years old", Dr Robert Larribau told the BBC's World Tonight programme.
"The fire broke out so intensely that burns can be internal. People breathed toxic smoke into the lungs," Dr Larribau said.
The president of the UK Association of Fire Investigators, Richard Hagger, described the "flashover" effect believed to have made the blaze so deadly.
"You'll start with a fire, the flames and the thermal radiation will go to the ceiling level and mushroom out across," he told The World Tonight.
"That thermal radiation then travels downwards on to other fuel packages, such as furniture, tables, raises the temperature to the point when they thermally decompose and produce flammable gas.
"And then that gas ignites, but it ignites at a fairly rapid rate. So the room, in effect, becomes a full room on fire within a matter of seconds."
The Italian Foreign Ministry told the BBC that 16 Italian nationals were currently missing, and between 12 and 15 others were receiving treatment in hospital.
The French foreign ministry said eight of its citizens were missing and that it could not rule out that French nationals were among the dead.
French media reported that at least two of the injured were French nationals.
Three Italian nationals were being evacuated to Milan's Niguarda hospital where there was a major burns unit, Italian councillor Guido Bertolaso said.
They have burns across "30-40% of their bodies", he told reporters, and they remained intubated, but "the fact they could be moved is a good sign".
The precise number of dead and injured is not yet known, nor their nationalities but officials have confirmed that several nationalities were involved.
Speaking at a press conference on Thursday evening, officials said they did not know how many people were in the bar when the fire broke out.
State councillor Stéphane Ganzer described the bar as having a "young festive population" during the New Year's Eve party.
