Three people are being treated for life-threatening injuries after the act in Vetlanda, where a perpetrator injured seven people.
The police are investigating whether there is a terrorist motive.
"Terrible news"
Danish Prime Minister Mette Frederiksen is one of the first world leaders to comment on the act in Vetlanda.
“Terrible news from Sweden.
These are acts that are being investigated as terrorism and that I strongly dissociate myself from.
We stand with the entire Swedish people and the Swedish government.
I send my warmest thoughts to Vetlanda, to the victims and their relatives ", she says.
"Follows developments with concern"
Ukraine's newcomer Foreign Minister Dmytro Kuleba described the attack as "terrible" and said "there is never any excuse for violence".
Italian MP Sabrina De Carlo also wrote on Twitter that she is following developments with concern.
International news
Several media companies in the Nordic region have reported on the act.
Among others, Norwegian VG, Swedish Yle in Finland and the Danish Jyllands-posten.
The attack is also receiving attention outside the Nordic region.
German media such as Der Tagesspiegel, British BBC and Spanish El País have written about it.
The news also reached Australian ABC news, which sent out a notice of the attack, to its mobile users.