According to police, the victims were two 17-year-old Danish girls and a 47-year-old Russian citizen. Two Danes and two Swedes are critically ill in the hospital.
A 22-year-old man, described as "an ethnic Dane," was arrested at Field's centre minutes after the shooting.
He had mental health issues, and there is no evidence of a terror motive, according to Police Chief Soeren Thomassen.
A judge will question the suspect, who has not been identified, on Monday.
Denmark, according to Prime Minister Mette Frederiksen, had been subjected to a heinous attack.
She stated that she wished to encourage Danes to unite and support one another during this difficult time.
"Our beautiful, usually safe capital was changed in an instant," she said.
Denmark was hosting the first three stages of the Tour de France for the first time when the deadly shopping mall attack occurred.
According to police, the suspect was arrested with a rifle and ammunition.
They have no evidence that other attackers were involved, and they have urged shop owners to save any video surveillance footage they may have.
Field's has over 140 stores and restaurants. The multi-story shopping centre is located on the outskirts of Copenhagen, directly across from a subway line that connects to the city centre.
As gunfire rang out, witnesses reported panic among shoppers.
"Suddenly, we hear shots," one of them, Isabelle, told Danish media. I think I heard ten shots before we ran through the mall and ended up in a toilet, where we huddled together in this tiny toilet with about 11 other people.
"It's really hot, and we're waiting and scared." It's been a dreadful experience."
A concert by British singer Harry Styles was cancelled at a venue less than a mile from the scene.
Crowds had already gathered inside the building.
"My daughters were supposed to see Harry Styles," Hans Christian Stolz, a 53-year-old Swede who arrived to pick up his children, explained to AFP. "They called to say someone was shooting, and they were in a restaurant at the time."
"At first, we thought people were running because they had seen Harry Styles, but then we realised it was people in panic... We ran for our lives," his daughter Cassandra explained.
"My team and I pray for everyone involved in the Copenhagen shopping mall shooting. I am shocked," Styles wrote on Snapchat.
Shortly after the shooting, the Danish royal family announced that a reception hosted by Crown Prince Frederik to commemorate hosting the first three stages of the Tour de France had been cancelled.
Several neighbouring leaders condemned the shooting and offered condolences to the victims' families.
Finnish Prime Minister Sanna Marin condemned the "shocking act of violence," while Norwegian Prime Minister Jonas Gahr Store said his "thoughts are with the victims and their families, as well as the relief crews who are currently working to save lives."
The last major terror event in Denmark occurred in 2015, when two people were killed and six police officers were injured during an attack on a cultural centre and a synagogue in Copenhagen.
After a shootout with police, the gunman was killed.
The country has some of the strictest gun laws in Europe, with licences to own firearms usually only available after background checks for hunting or sport shooting - and an almost total ban on automatic weapons. It is illegal to carry a firearm in public.