"What we've seen recently is that everything from mosques to individuals are being attacked - especially Muslim women, who are often wearing a shawl. We know this from experience," says Mohammed Kharraki, spokesperson for the association.
Following the Charlie Hebdo murders, several mosques have been attacked in France.
Professor Göran Larsson, an expert in religious studies at the University of Gothenburg, told Swedish Radio that the risk of attacks on Muslims is likely to increase following the Paris attack.
"Research and experience of previous events clearly shows that what happens on the international arena, on the global arena often has consequences at the local level, even in Sweden. So it's not unreasonable to think that tensions could rise and in the worst cases this can lead to different types of attack or abuse," said Larsson.
The Swedish Security Service, Säpo, echoed the call for raised awareness, saying in a statement that "something serious could happen in Sweden."
Speaking to Swedish Radio, operations chief at Säpo, Anders Kassman, said however that events in Paris had not prompted the service to raise Sweden's terror threat level.
The TT news agency has since reported that a mosque in Mariestad has been attacked. According to the Expressen newspaper, a window was smashed with a can of meat and the words "go home" have been daubed on one of the mosque's walls.