A lorry drove down the pedestrian Drottinggatan street in central Stockholm just before 3pm on Friday and crashed into the Åhléns department store.
Four people are confirmed dead, according to preliminary information from the police.
One person had died in hospital, the Stockholm County Council Medical Director Johan Bratt confirmed to Swedish Radio on Friday evening.
15 people are injured, nine of whom are seriously injured. Two of the injured are children.
The lorry used in the presumed attack belongs to the Spendrups brewery, and was stolen outside a restaurant in central Stockholm minutes before the deed.
One person arrested
At a press conference in Stockholm at 9.15pm on Friday, the police stated the incident is being treated as a terror attack.
A man was arrested in the northern Stockholm suburb of Märsta on Friday evening for some kind of involvement in the deed, the police confirmed at the press conference.
The police had earlier released CCTV footage of a man wanted for questioning in connection with the suspected attack. The picture showed a man clad in a hooded jacket on an escalator in what appears to be the Stockholm metro. The police stressed he was not suspected of the deed, but was wanted for questioning.
At the press conference on Friday evening, the police confirmed the man arrested is thought to be the person captured on CCTV. He is not thought to be the person who drove the lorry.
Prime Minister suspects terror attack
Prime Minister Stefan Löfven was on his way to Gothenburg when the suspected attack took place, but returned to Stockholm. At 9.30pm he spoke at a government press conference.
"My thoughts are first of all with the victims and their families. In this difficult moment, Swedish authorities, including the police and hospitals, are doing everything they can to save lives and maintain our safety," Löfven said.
When asked what the event would mean for Sweden if the deed should turn out to be a terror attack, the prime minister responded:
Terrorists want us to be afraid, want us to change our behaviour, want us to not live our lives in a normal way. But that is what we are going to do. Terrorists can never defeat Sweden. Never."
Major traffic disruptions
The police have urged people to stay away from central Stockholm while the investigation is ongoing.
Public transport in Stockholm was still suffering major delays at 9pm, after having been cancelled for several hours.
National train services to and from Stockholm's Central Station were cancelled for several hours, but were resumed again late on Friday evening, with major delays.
This has happened:
- At 2.53pm the police were alerted about a lorry having rammed several people in a busy street in central Stockholm.
- At least 4 people are dead. 15 people are being treated in hospital for their injuries.
- One person was arrested on Friday evening.
- There is no confirmation about the incident being a terror attack, the Swedish Security Service said.
- However, at a press conference Prime Minister Stefan Löfven said: "Everything indicates this is a terror attack."
- Large parts of central Stockholm were cordoned off. Several shopping centres across the city were evacuated.
- Trains passing through Stockholm's Central Station were cancelled for most of the afternoon and evening. Services were resumed late on Friday evening, but with major disruptions.
- Metro trains were taken back into service late on Friday evening, but did not stop at the Central Station, and were subject to severe delays.
- The parliament building (Riksdag) and the government headquarters Rosenbad were in lock-down for much of the afternoon, but were later evacuated.