The Independent Police Complaints Authority said in a statement that the 25-year-old man identified by local media as Mesa Hodzic "died overnight in Rigshospitalet (hospital) from his injuries."
The agency is currently investigating the incident because of police use of guns during the arrest.
According to local media reports, Hodzic had had links to an extremist group named as Millatu Ibrahim.
Hodzic also sympathized with Daesh, which is currently committing crimes against humanity in Syria and Iraq.
However, there is no evidence, as of yet, that the shooting during the police anti-narcotics operations late on August 31 in Copenhagen’s Freetown Christiania neighborhood had been motivated by his extremist ideology.
During the raid, Hodzic, who was a naturalized Dane originally from Bosnia and Herzegovina, shot two police officers, critically injuring one of them, as well as one civilian.
Hodzic, himself, sustained the wounds in a later police shootout during his arrest in a suburban area outside Copenhagen early Thursday.
Criminal gangs run a drug trade in the notorious Freetown Christiania area, where hippies established a self-governing squatters' commune in deserted army barracks decades ago.
On Friday, local residents tore down the open air stalls used by the drug dealers and urged the public to stop buying drugs in the area with a long history of widespread drug trading activities.