“We now know that there are several dead,” Copenhagen police chief Søren Thomassen told journalists in a press conference on Sunday evening.
The shooting happened at the large Field’s shopping mall in the Amager district between the city centre and the airport.
“We are investigating this as an incident in which we cannot rule out terrorism,” he said adding that it was too early to talk about a possible motive.
Thomassen said the suspect arrested over the shooting was as “ethnically Danish” and police believe he acted alone.
The exact number of deaths and injuries had not been confirmed by police.
Some witnesses had described the gunman as a man around 1.8 metres tall carrying a hunting rifle.
Danish police also did not say whether the suspect was previously known to them nor any details about the weapon used.
Thomassen said shots had been fired in several locations inside the shopping centre.
Police said they have initiated a major operation to ensure there are no additional gunman besides the arrested individual.
Until this can be confirmed, a wider police operation was taking place, Thomassen said.
“We must be completely certain that we have this situation under control,” he said.
“This is a massive operation. And it’s not just in Copenhagen, it’s all of Zealand,” he said.
“We have no information currently that can confirm this happened in cooperation with others,” Thomassen said.
Police reinforcements were deployed around the large Field’s mall in the Amager district, Copenhagen earlier police wrote on Twitter.
“We’re on the scene, shots were fired and several people have been hit,” they said.
Images from the scene showed women carrying their children and ambulance personnel carrying people away on stretchers.
“Terrible reports of shooting in Fields. We do not yet know for sure how many are injured or dead, but it is very serious,” Copenhagen’s mayor, Sophie Andersen, said in a post to social media.
According to public broadcaster DR, at least three people were being treated in hospital.
Eyewitnesses quoted by Danish media said they saw more than 100 people rush towards the mall’s exit as the first shots were heard.
“We could see that many people suddenly ran towards the exit and then we heard a bang. Then we ran out of Field’s too,” Thea Schmidt, who was in the mall at time of the attack told broadcaster TV2.
Another witness named Isabella told DR: “All of a sudden we heard gunshots, I heard 10 shots, and we ran as far as
we could to take refuge in the toilet.
She said she had hidden in the mall for two hours.
Police had urged people in the building to wait inside for their arrival and called on others to keep away from the area.
In addition, police asked that witnesses get in touch with them and called on those that had visited the shopping mall to contact their relatives.
At around 6:30pm, roads around the mall were blocked, the subway was stopped and a helicopter was flying above, according to an AFP correspondent at the scene.
Heavily armed police officers prevented onlookers from approaching and locals from returning to their homes.
The attack occurred two days after this year’s Tour de France cycling competition started took off from Copenhagen, and the Tour organisers released a statement expressing their sympathy.
“The entire caravan of the Tour de France sends its sincerest condolences to the victims and their families,” it said.
At the nearby Royal Arena, a concert with British singer Harry Styles was scheduled in the evening.
Shortly after the shooting the organiser announced it would “proceed as planned,” but later announced its cancellation, following criticism.
“My team and I pray for everyone involved in the Copenhagen shopping mall shooting. I am shocked,” Styles said in a Snapchat post.
The shooting comes just over a week after a gunman opened fire near a gay bar in Oslo in neighbouring Norway, killing two people and wounding 21 others.
In February of 2015, two people were killed and five injured in Copenhagen in a series Islamist-motivated shootings.