The man, 24, was arrested on Tuesday evening, police said in a statement released on Wednesday. He is not a Swedish citizen, but has been in Sweden for at least a year. The man had previously figured in an unconnected police investigation.
He lives in western Gothenburg, and a warrant had been put out for his arrest earlier on Tuesday. His arrest was described by police as "undramatic".
Ivanisevic was found dead in the Gothenburg home of the family for whom she worked.
The victim's family have been informed of the development, police say.