"At this time it is unclear how the fire started. A preliminary investigation for arson has been launched and the premises have been cordoned off to allow the technical staff to work," police said in a statement.
Firemen and police were called in at around 3:00 am (0200 GMT) but they found no one at the site in the town of Boras.
"It is no longer possible to use the site. All activities have been cancelled until further notice," the mosque's administration said on Facebook, AFP reported.
Arsonists have targeted several mosques and centers housing asylum seekers in recent months, in a string of attacks linked to the growing influx of migrants.
Sweden, which is home to 9.8 million people, is one of the European Union countries that has taken in the largest number of refugees in relation to its population.
Support for the far-right has mounted as Sweden's ability to house and integrate the new arrivals comes under strain.