Their injuries are described as serious but not life threatening. They have been taken to hospitals in Mora and Falun.
Five men were located in a nearby vehicle and arrested on suspicion of aggravated assault.
The stabbings occurred during a fight which broke out at 1:30am early Wednesday morning.
All of those involved in the incident are in their twenties, according to the Dala police department.
Rättvik is currently the scene of an annual Classic Car Week ‘cruising’ event, which brings many visitors to the small town in Dalarna.
According to the Dalarnas Tidningar news website, police reported several detentions due to drunkenness and rowdy behaviour throughout the night.