The vehicle drove into crowds on Drottninggatan (Queen Street) – one of the city’s major pedestrian streets, just before 3pm local time, before crashing into Åhlens Mall.
Armed police are currently at the scene and the incident is being treated as a suspected terror attack, according to local media.
The lorry had been hijacked earlier in the day.
The public has been warned to stay away from the city centre and a police cordon has been put up around the area.
Swedish Prime Minister Stefan Lofven has said everything indicates that the Stockholm truck crash is “a terror attack”.
He added: “The Government is naturally being updated continuously and receiving the latest information.
“The Government is assisting the authorities in its work and now we are encouraging the public to be alert and listen to the police’s information.”
At least two people have been arrested by police – The first arrest was made at Olof Palmes gata and the other at Klara North Church Street.
Shops on the street have closed down and people are being locked inside, according to reports.
One woman wrote on Twitter: “Friend are trapped at the dentist at fridhemsplan. Police say it is anxiously outside.”
Armed police are at the main railway station in Stockholm, according to reports from Aftonbladet.
A witness reported seeing the driver of the truck wearing a mask.
Stockholm’s Parliament has been evacuated and the area cordoned off. At least eight people are said to be injured.
The public subway system has also now been stopped in the city and an evacuation of the Central Train station in Stockholm has been ordered.
The area is the main shopping area of Stockholm and is a very busy area of the city.
Map of area
He said: “I saw at least three dead, but there are probably more. It’s a complete mess here.”
Several people are lying lifeless in the street according to witnesses, Expressen.se reported.
Towe Hägg of Stockholm police said: “We have have had the reports and have initial information about person injuries.”
Reports suggest the vehicle rammed through the crowded street drove into Åhlens Mall.
Police have reported multiple casualties after the Stockholm truck attack
Jan Granroth was inside a shoe store on Drottninggatan when he heard people starting to scream.
Government sources confirmed Swedish Prime Minister Stefan Lofven is currently in Gotherberg and is returning to Stockholm immediately to after the horrifying attack.
King Carl XVI Gustaf of Sweden said in a statement: “I and the entire royal family are dismayed at the information about this afternoon’s attack in Stockholm.”
Paramedics attend to the injured in Central Stockholm
The attack took place at the Ahlens department store at Drottninggatan