The zoo says it cannot keep the giraffe, named Marius, because of European rules to avoid in-breeding, and that attempts to find it a new home have failed.
Copenhagen Zoo says it needs to kill the giraffe before it becomes an adult and attempts to mate.
Campaigners say to do so would be barbaric.
Bengt Holst, scientific director at the zoo, said 18-month-old Marius’s genes were already well represented among giraffes at the zoo.
He could not understand the fuss Marius’s impending destruction had generated, pointing out that, for instance, 700-800 deer are killed every year at a deer park north of Copenhagen to control their numbers.
Marius is due to be killed by a bolt gun. The zoo will not use a lethal injection, because that would contaminate the meat.
The zoo plans to dissect the animal after it has been killed, before feeding it to the tigers and other carnivores.
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