Two of the people taken to hospital were children. The person who died in hospital lived in the apartment where the fire is believed to have started, Stockholm police told Swedish Radio News.
"We were informed of a fierce fire in an apartment which was still very active when we arrived. We had a very acute life rescue operation," fire engineer Mats Körner tells TT.
Around 30 people were evacuated from the building, some of them directly from their balconies, as the straiwell was full of smoke, according to news agency TT.
The fire was controlled around noon and the cause is still unclear.