"There are several injured, and what we also know now is that there are several dead," Chief Police Inspector Soren Thomassen told journalists, adding that police had launched a massive search operation throughout the local Zealand region.
Thomassen declined to speak about the suspect's potential motives and whether he was known to police.
Copenhagen police said officers had been sent to Field's mall in the Danish capital late on Sunday afternoon after reports of a shooting, and had told people inside the centre to stay put and await assistance.
There was currently no indication that other shooters had been present, police said.
The capital's main hospital, Rigshospitalet, had received a "small group of patients" for treatment, a spokesman told Reuters. It had called in extra staff, including surgeons and nurses, the spokesman added.
Local media published images showing heavily armed police officers at the scene, as well as people running out of the mall. Footage published by tabloid Ekstra Bladet showed one person being carried by rescue workers into an ambulance on a stretcher.
"He is just shooting into the crowd, not up in ceiling or into the floor," she added.
The huge multi-storey shopping mall has shops, restaurant and parking, and is located around 5 kilometres (3 miles) south of downtown Copenhagen.
The attack follows a deadly shooting in neighbouring Norway last week, in which two people were killed by a lone shooter in the capital Oslo.
The terrorist threat against Denmark is currently assessed to be "serious", with the biggest threat coming from "militant Islamism", according to the latest report from the Danish Security and Intelligence Service.
The threat to Denmark from rightwing extremists is considered at a "general" level, which means there is capability and/or intent and possibly planning.
Denmark last saw a militant attack in 2015, when two people were killed and six police officers were wounded when a lone gunman shot and killed a man outside a culture centre hosting a debate on freedom of speech, and later killed a person outside a Jewish synagogue in central Copenhagen.
The gunman was killed in a shoot-out with police.
An event in Southern Denmark to commemorate the end of the first three stages of the Tour de France cycling race, hosted by the Danish Crown Prince and with Prime Minister Mette Frederiksen in attendance, had been cancelled late on Sunday, the Royal House said on its website.