Marius, an 18-month-old giraffe, was put down with a bolt gun early on Sunday, zoo spokesman Tobias Stenbaek Bro confirmed.
The body of the giraffe, which was killed in a bid to prevent in-breeding, will be chopped up and fed to carnivores at the zoo.
"It was put down at 9:20. It went as planned. It's always the people's right to protest. But of course we have been surprised," Stenbaek Bro told AFP.
The zoo explained that it had no choice other than to prevent the animal attaining adulthood.
Under European Association of Zoos and Aquaria (EAZA) rules, in-breeding between giraffes is to be avoided.
Although Marius is healthy, his genes are already well represented at the zoo and he cannot be taken in by the 300 other EAZA-affiliated zoos.
Castration is considered cruel with "undesirable effects", while releasing him in the wild is thought unlikely to succeed.
Why was relocation not considered?!! Many offers were put forward to relocate Marius to other zoos, Copenhagen turned them all down!! Why?
Surely we need to be more responsible in breeding animals in our care , so it never comes that we need to put them down> Especially animals that in their own natural environment are at risk from habitat encroachment and other human factors.