Twenty-two children were killed in the accident, which happened when the bus inexplicably swerved and hit a concrete wall while traveling through a tunnel. Another 24 children were reported injured in the crash.
The impact of the crash was so violent that the front of the bus was seriously damaged, trapping many of the passengers, police said.
Most of those on the bus, from two schools in Belgium, were aged around 12.
Belgium was plunged into mourning following the news of the crash.
"This is a tragic day for all of Belgium," said Belgian Prime Minister Elio Di Rupo, adding that he would be traveling to Switzerland on Wednesday.
Police and fire services turned out in force to seal off the scene of the accident, closing the tunnel at both ends, as a fleet of helicopters and ambulances ferried the injured to four hospitals.
Fire crews had to cut free some of the victims from the tangled mass of wreckage.
The coach, which was carrying 52 passengers, was traveling from Val d'Anniviers towards the Swiss town of Sion on the A9 motorway when the accident happened at 9.15 pm on Tuesday (2015 GMT).
In Brussels, the Belgian foreign ministry said the coach was one of three hired by a Christian group. The students came from two different schools: in Lommel in northeast Belgium and Heverlee in the center.
The Dutch ANP news agency quoted the fire services Chief in Lommel as saying that seven children from the Netherlands were on the bus.
During a press conference early on Wednesday, the Valais canton police commander said the tragedy was "unprecedented" and that even seasoned rescuers had been traumatized.
Surgeon Jean-Pierre Deslarzes said in one of the hospitals "All the rescuers were shocked by what they have experienced."
Belgium's ambassador in Switzerland Jan Luykx went straight to the site of the accident.
"This tragedy will hit the whole of Belgium," he told the Swiss news agency SDA-ATS. "The magnitude of the accident is difficult to digest ... for the moment I am concentrating on the practical aspects.
"The emotional side will come when we meet with the families," he added.
Belgian authorities said were doing everything they could to ensure that the families of the victims were kept informed and treated with dignity, the prime minister's office said.
Foreign Minister Didier Reynders told RTBF radio two army aircraft would be used to fly the relatives to Switzerland.
"There are two planes ready to take off," at the military airport in Melsbroek, near Brussels, he said.
"The aim is to accompany the families who want to go to Switzerland," said Reynders, who was speaking from Vietnam where he is on an official visit.
A psychological support team was also on hand, he added.
"Our first thought was the distress of the families," he said.
Peter Vanvelthoven, the mayor of Lommel in northeast Belgium, where some of the schoolchildren went to school, said they were also trying to help the families.
"We have arranged a reception at the school, first for the parents, for the children and for the teachers, too," he said.
At Heverlee, near Louvain, home to some of the other crash victims, the atmosphere was fraught, RTBF reported -- all the more so because it was not yet known who had died and who had survived.
The families of the victims were gathered at the Sint-Lambertus School, while the students had been taken to another school.
"I'm at a loss for words.Terribly hurt, terribly moved".Transport Minister Melchior Wathelet told RTBF radio.
"We are all thinking like parents, with this terrible thought for those parents who will not see their children coming back today," he said.
"Yesterday evening, they were looking forward to seeing them and they won't see them again."
It was unclear what caused the bus to swerve to the right, mounting the kerb before hitting a concrete wall at the end of an emergency lay-by. The accident happened between the east and west exits from the city of Sion.
Six adults were among the dead, including the two drivers of the coach, said police.
The Belgian transport company that ran the coach that crashed was Toptours, based in Aarschot, central Belgium, said Wathelet.
"The company ... enjoys an excellent reputation," he added.
"It has always respected the rules," regarding safety, he added.
The two coach drivers had arrived in Switzerland the day before. The coach had been built in 2002.