When the police arrived at the scene, a 35-year-old man was arrested. He has now been taken into custody.
According to the police, he is suspected of, among other things, attempted arson and vandalism.
According to local Swedish newspaper Blekinge Läns Tidning, a man was lying in the square in Sölvesborg and shouting Nazi slogans for more than an hour during the night.
Preliminary investigation leader Nina Ljung at the Swedish Prosecution Authority did not comment on the motive for the incident.
"Both we and the police are carrying out a number of investigative measures now to try to get a clearer picture," she told Swedish newswire TT.
She did not want to say whether the attack may have been pre-planned.
"It is far too early to comment," she said.
The Social Democrats have called the incident a "Nazi arson attack".
"It is not just an attack on our party premises in Sölvesborg. It is an attack on Swedish democracy as a whole. It is completely unacceptable," said party secretary Tobias Baudin in a written comment.
Sölvesborg, where the incident took place, is home to Sweden Democrat leader Jimmie Åkesson, who is currently doing an election boat tour on the Göta canal.