"We will wait before we go public with the gender and the age. But unfortunately one person has died in this accident. The person died at the scene," police spokesperson Peter Adlersson told the TT news agency.
The accident occurred just before 7.30am on Motorway 27, which is south of Tranemo in the west of the country.
Emergency services were immediately called to the scene to tend to the injured.
The bus was carrying 52 passengers: 20 were taken to a hospital in Tranemo, while 20 others "with less serious injuries or just shock" were taken by ambulance to a hospital in Borås, a press spokesperson for west Sweden police told The Local.
Two people were trapped inside the bus for more than an hour before emergency services were able to get them out. Rescue workers at the scene described the accident as "extremely serious."
TV4 news reported just after 11am that at least one person had died as a result of the crash. A further nine people have been listed as critically injured.
"We have had several ambulances and an ambulance helicopter on the site," Peder Liljeroth from the local fire service told the TT news agency.
West Sweden police told The Local it initially appeared that all of the people on the bus were from Sweden rather than abroad. They were understood to be travelling over the border to Denmark.