"Two suffer from smoke inhalation, two have cuts and bruises and one has a fracture", says Lars Franzell, who is heading up the investigation at Eskilstuna police. He tells news agency TT they are investigating the case as aggravated arson.
A press release from the Mälarsjukhuset hospital says one person is "hurt badly but stable".
The fire started after 1 pm on Christmas Day in a prayer room housed in a tower block.
Swedish television SVT says a witness told them a man with a bottle of petrol was seen near the room's entrance just before the fire broke out.
Police say to news agency TT the fire started when an object was thrown through the window.
It is the Somali association that uses the room, and they were having prayers today.
Around 20 people were inside, including children.
All the apartments have been cleared of people. They are being housed in a nearby youth centre.
It took a while for emergency services to evacuate the apartment block, as there was too much smoke on the stairs. People were advised to keep their doors closed and keep out the smoke, until they can be rescued.
Police have visited nearby homes and questioned people - they say to news agency TT they have no suspect yet.