At least a dozen people were also injured in the incident on Drottninggatan (Queen Street), one of the city's major pedestrian streets, on Friday afternoon.
Swedish Prime Minister Stefan Lofven said it was a terror attack.
One man has been arrested, after police released a CCTV image of a person who may be connected to the case.
In a speech on Friday night, Mr Lofven said Swedish values of democracy and freedom would not be "undermined by hatred".
He also announced the country's border controls had been strengthened.
The crash happened at the Ahlens department store just before 15:00 local time (13:00 GMT). Witnesses say the lorry drove into the front window.
One eyewitness, Annevi Petersson, told the BBC she was in the shop's fitting room when she heard the screams. "There was blood everywhere," she said.
Swedish brewery Spendrups said its lorry had been stolen on its way to a restaurant delivery earlier in the day.
"Someone jumped into the driver's cabin and drove off with the vehicle while the driver was unloading," a brewery spokesperson told the TT news agency.
The shop sits close to the city's central station, which was evacuated.
The metro, central roads and various bus lines were also shut down after the attack.
Shots were reportedly fired in another part of the city, but Swedish police told local media there was no connection between the two incidents.
City authorities said they had made several spaces, including a number of school buildings, available as temporary accommodation for those who could not get home because of transport disruptions.
They have also asked people not to share photographs of the victims online.
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