No-one was reported hurt in the blaze, which started around 3 am at a mosque in the southern town of Eslov, police said in a statement.
The fire was quickly put out and caused only minor damage, it said.
While police said the cause was under investigation, a fire department spokesman said it appeared to be an act of arson.
"There is no possible natural explanation for this type of fire to break out" by itself, Gustaf Sandell told public radio.
Sweden, known for tolerance and refugee-friendly policies, saw an extreme right party, the Sweden Democrats, become the third-largest force in parliament in legislative elections in September.
In early December, the party brought down the government after less than three months by refusing to back its budget proposal in parliament.
On Saturday the government announced it had reached a deal with the opposition that will enable it to remain in power and to avert the Nordic country's first snap elections in more than half a century, but the far right has threatened to hold a no-confidence vote.
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