The incident happened in an area of Goteborg, Sweden's second largest city, with a history of gang-related violence, police spokesperson Ulla Brehm said, adding there were indications the shooting was gang-related, Sputniknews reported.
"There is absolutely nothing that indicates terrorism," she added.
One witness told Swedish media that two men entered the restaurant and started shooting with automatic weapons, the Associated Press reported.
The eight wounded people have been hospitalized.
According to the police, the death toll could be expected to rise.
Gothenburg police spokesperson Ulla Brehm was quoted by SVT as saying that there were indications the crime could be related to the gang activity in the area.
No suspects have yet been arrested by the police.