Emergency service were alerted to the blaze shortly after midnight. The fire was quickly brought under control but the roundabout was temporarily closed for traffic due to the risk of the structure collapsing.
The wooden 'roundabout dog' was constructed by Lars Vilks together with a group of high school students from Trelleborg. When completed in June of this year, the seven-metre canine was erected in the middle of a roundabout on the outskirts of the town.
Police said they were classifying the crime as vandalism and did not yet have any supects.
Earlier this year, Sweden was gripped by a 'roundabout dog' craze - hastily constructed wooden dogs began appearing in the middle of traffic circles nationwide as an alternative to the often unpopular and costly public artworks commissioned by local councils.
Lars Vilks' contribution to the guerrilla art movement has been subjected to several arson attempts since the publication in Nerikes Allehanda of a cartoon depicting the Muslim prophet Muhammad as a roundabout dog.
Seemingly unfazed by the furious reactions to his drawings, the controversial artist indicated at one point that he was also considering constructing an actual roundabout dog featuring the founder of Islam.
Earlier this week, a woman in western Sweden was formally charged with having issued the artist with a death threat via e-mail.
"The person in question has admitted to us that she sent the e-mail," said police spokesman Håkan Lund.
"What is more worrying is that she stands by her words, explaining that her beliefs and convictions had been desecrated and attacked," he added.
According to police, the woman - described as a devout Muslim with a family - was not part of any militant networks.
She did not say that she would personally kill Lars Vilks but she encouraged others to do so.
"There are a lot of people on the internet expressing this same will and intention," said Lund.