Police rushed to the scene after receiving reports of a shooting in the south-western Hvidovre suburb shortly after midday, newspaper Ekstra Bladet reported.
"She was shot several times, but we don't know exactly how many," police spokesman Carsten Jansson told the newspaper. "She had a number of gunshot wounds to her chest."
By the time police arrived, passers-by were attempting to resuscitate the woman. She was pronounced dead at 12.30pm.
Police suspect the woman was killed by her ex-husband. After releasing his identity and asking the public for leads, they were able to arrest the man.
The 33-year-old suspect was arrested on the Amager Motorvej shortly after 4pm.