Firefighters were called to the blaze in Eskilstuna, 90 kilometres (50 miles) west of Stockholm, around 11:00pm (2100 GMT) on Friday, but the building was almost totally destroyed, AFP reported.
Police have launched an arson inquiry into the attack on the building, a former holiday camp which had been set to house around 60 people seeking asylum in Sweden.
The incident adds to around a dozen similar attacks since the start of the year and came a day after a man armed with a sword killed two people in a racist attack at a Swedish school with many immigrant pupils.
“If it’s because of the fact that some people think this type of lodging should not exist – then that’s really terrible,” local official Tryggve Lundh said of the migrant hostel fire on SR public radio.
Sweden, a country of 9.8 million, expects to receive up to 190,000 asylum applications this year – putting it among the EU states with the highest proportion of refugees per capita as the continent struggles with a massive influx of migrants.
Anti-immigration attitudes have been rising across Europe, as more than 600,000 migrants and refugees – most fleeing war in Syria, Iraq and Afghanistan – have made the dangerous journey to the continent this year, according to the UN.