Swedish artist Lars Vilks - the author of controversial Prophet Mohammed cartoons that sparked worldwide protests in 2007 - was among those at the debate targeted by two gunmen who then fled the scene.
Danish Prime Minister Prime Minister Helle Thorning-Schmidt described the assault as "a terrorist attack" as Danish televion showed the windows of the Krudttonden cultural centre pock marked by multiple bullet holes.
French ambassador to Denmark Francois Zimeray, who had been present at the debate but was not hurt, told AFP the shooting was an attempt to replicate the Charlie Hebdo killings in Paris.
"Intuitively I would say there were at least 50 gunshots, and the police here are saying 200," he told AFP.
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"Bullets went through the doors and everyone threw themselves to the floor."
A statement by Danish police said "an unidentified man died after having been hit by bullets" in the strike, and three officers were wounded in the shooting.
Police also said the Volkswagen Polo the two suspected assailants fled the scene in was found abandoned around two hours after the attack.
The assault comes at a time of heightened security and rising fears of Islamist attacks, following January 7 and 9 incidents in Paris that left 17 people dead.
A series of anti-terror sweeps have been carried out across Europe since mid-January, resulting in the arrests of dozens of suspected jihadist and seizures of large stocks of weapons and explosives.
Charlie Hebdo raised the ire of Islamist extremists by republishing cartoons by Vilks and other caricatures, and periodically satirising Islam on its own in later editions.
French Foreign Minister Laurent Fabius condemned what he called a "terrorist attack targeting a public meeting", saying in a statement that France "remains by the side of the Danish authorities and people in the fight against terrorism."
The French president's office said Interior Minister Bernard Cazeneuve was headed to the scene.