Emergency services were called to the mosque in Eslöv, a small city in the south of the country, at around 3.15am on Monday.
It is understood that the blaze began after flammable liquid caught fire in one of the rooms in the building.
Firefighters quickly arrived at the scene and were able to prevent the fire spreading, although the flames still caused minor damage to the building. Firefighters suspect foul play.
"There is no possible natural explanation for this type of fire to break out by itself", fire department spokesman Gustaf Sandell told Sveriges Radio.
Samir Muric, the local imam, said he was worried for his own safety.
"Unfortunately, this is probably something to do with Islamophobia. I live close by and it's beginning to feel unsafe," he told the TT news agency.
Police officers cordoned off the area and have launched an investigation. Photo: TT
The local fire brigade said that with residential homes on top of the mosque, it was lucky that they were able to quell the blaze before more damage was done.
"Think of all the people who lived above," added Muric. "Think how shocked they must be. I notice that people are scared."
"I've already noticed that fewer people are coming to the mosque with all the vandalism. I can only imagine how an arson attack will affect this."
Local Social Democrat councillor Johan Andersson said the blaze left him "angry".
"This is totally unacceptable. This is both a threat to individual people in their home and a serious act against a religious building," he explained.
Mosques in Sweden have been subject to growing numbers of attacks in recent months.
The fire comes less than a week after several people were hurt in a separate fire at a mosque in Eskilstuna in central Sweden on Christmas Day. Police say they are unable to confirm whether the blaze there was started on purpose.
Sweden, known for tolerance and refugee-friendly policies, saw a nationalist right party, the Sweden Democrats, become the third-largest force in parliament in legislative elections in September and reports of race-related violence are on the rise in the country.
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 country's first snap elections in more than half a century, but the far right has threatened to hold a no-confidence vote.