Police said violence flared after an altercation between revellers at a nightclub in the area around Gothersgade and Borgergade in the city. Officers investigating the attack said they had arrested a man and were continuing to question him. Forensics teams are carrying out crime scene investigations and witnesses are being interviewed.
Deputy Police Inspector Allan Teddy Wadsworth-Hansen said there was nothing to suggest the knife attack was gang-related.
He said: “Based on the indications we have so far, there are some discrepancies between some disco guests who have unfortunately ended up with this very tragic outcome.”
Local media said large parts of the city centre were sealed off while the investigations continue and reported a large armed police presence.
Some public transport service have been affected by the disruption and road closures.
Police said parts of Copenhagen’s Kultorvet were also closed after reports of a separate knife attack.
Copenhagen Police investigator Søren Lauritsen said: “At present, we cannot say whether the two episodes are related. We are still investigating this.”