About 60 others were injured in the blast which started a blaze in the mall, according to the authorities.
Part of the mall's roof also collapsed.
At the time of the explosion the shopping centre - one of the largest in the region - was full of customers doing their weekend shopping, and eyewitnesses have spoken of gruesome scenes with blood and body parts littering the scene of the accident.
Floor shook
The cause of the blast is not certain, but reports say it is likely to have been an accident.
Rescue services said the blast had been caused by gas cylinders at the Myyrmanni Shopping Mall in Vantaa, north of the capital.
But Jyrki Karjalainen, director of City Con which manages the mall, said there normally should not have been any gas cylinders or containers in the building.
Hospitals were put on alert following the explosion at 1930 local time (1630 GMT).
Witness Jami Koskimaka, said: "It was not a small explosion. The floor was shaking."
Antonia Kohl-Makkonen, said: "We were just talking that you should never go shopping on a day like this because of the peak hour.
"Suddenly an enormous bang was heard, actually an explosion and we thought that was a bomb. We left straight away, the situation was chaotic