The knife attack occurred on Wednesday afternoon at Donner's place in Visby - in the middle of the ongoing politician week in Almedalen.
A woman in her 60s was seriously injured and taken to hospital.
A few hours later, the police announced that the woman had died from her injuries.
In connection with the act, a man in his 30s was arrested near the crime scene.
Participated in NMR demonstrations
The man suspected of the knife attack is said to have been active in the Nazi Nordic resistance movement for several years, according to information to SVT as well as to Expressen and Aftonbladet.
Among other things, he is said to have been a recurring writer for the organization's online magazine Nordfront and participated in NMR's demonstrations.
According to information, the man was previously unpunished.
He is now arrested on probable cause on suspicion of murder.
The police currently do not want to comment on suspected motives and say that they do not know if there is any connection between the victim and the suspected perpetrator.
- That we are looking broadly and possibly for more people involved is a matter of course, says Fredrik Persson, police area chief on Gotland.
According to information, the perpetrator has connections to right-wing extremist groups. Can you confirm that?
- No, I can not confirm it because it is part of the investigation we are carrying out, says Fredrik Persson in SVT's Aktuellt.