The officer was reporting to work at the Albertslund police station when he was shot in the head.
Police said that the injured officer’s health deteriorated during the late afternoon and evening on Tuesday.
Doctors had initially said that shot officer’s condition was serious but they did not believe his life was in jeopardy.
He was declared dead at 2.18 on Wednesday afternoon.
“I communicate this with the greatest sorrow,” said Copenhagen Vestegn Police director Kim Christiansen in a statement.
“My thoughts go to the police officer's relatives and his many colleagues, who in the last day have shown great professionalism at this difficult and dark time.”
The officer was shot in the head at 8.20am on Tuesday as he was reporting to work.
Police arrested a 26-year-old Danish man who they say is mentally unstable. No motive for the shooting has been revealed.
“We will look closer at this whole thing over the next couple of days,” police inspector Svend Foldager said at a Tuesday press conference.
Foldager said that police believe that the shot officer was a random target.
“I cannot see how one would have predicted that that particular officer would have been standing at that ramp by that car. It is impossible, so it was a coincidence,” he said.
On Tuesday it was revealed that the weapon used to shoot the police officer, a .22-calibre pistol, had been stolen from a marksman’s club in nearby Rødovre. The gun was stolen on Monday and the club immediately reported the theft to police along with the name of the shooting suspect.
The 26-year-old man was a member of the Rødovre Skytteklub but police said that he did not have a licence to carry or operate a fireman.
The suspect is due to make a preliminary court appearance on Wednesday.