Police confirmed the accident via their website on Sunday morning.
The cause of the accident is not known at the time of writing.
“But [conditions] are very bad at the site, which may be something to do [with the accident],” Bergslagen Police spokesperson Tommy Lindh told TT.
Sweden has seen exceptionally cold temperatures across the country throughout the last week.
One of the two wounded passengers is reported to have sustained a head injury.
The road was temporarily closed while a recovery operation took place at the scene. A replacement bus has been sent to collect the remaining passengers.