Copenhagen police tweeted that officers had been sent to the Field's mall after reports of a shooting, and asked people to send footage and other relevant details from the scene.
Local media published images showing heavily armed police officers at the scene, as well as people running out of the mall.
The police did not provide further information about the arrest, or say how many had been injured. They advised people inside the centre to stay put and await police assistance, and asked other people to stay away from the area.
British singer Harry Styles was due to perform later in the evening, at 8 p.m. (1800 GMT), at a concert venue less than a mile from the mall.
The concert will go ahead as scheduled after close dialogue with the police, and half of the audience has already entered the venue, the concert promoter Live Nation said in an emailed comment to Reuters.
(Reporting by Stine Jacobsen and Nikolaj Skydsgaard; Editing by Kevin Liffey and Jan Harvey)