The knife attack occurred on Wednesday afternoon in the middle of Almedalen Week at Donners place in Visby.
The victim, the 64-year-old chief physician and psychiatric coordinator Ing-Marie Wieselgren, was first taken to hospital, but was confirmed dead later that evening.
Participated in NMR demonstrations
The man suspected of the murder is 33 years old.
He was arrested near the crime scene and, according to information to SVT, has connections to the Nazi Nordic resistance movement, NMR.
The man must have been active in NMR for several years, according to information to SVT, Expressen and Aftonbladet.
He is also said to have participated in their demonstrations and written for their online magazine Nordfront.
Acknowledged murder
The man, who has previously been unpunished, has been arrested on probable cause on suspicion of murder.
On Thursday morning, the perpetrator's defense lawyer Staffan Fredriksson informed Expressen that the man admits the crime.