Zoo officials said they decided to put down the 18-month-old male giraffe, named Marius, because of concerns about inbreeding, the Copenhagen Post reported. The giraffe was then fed to other zoo animals, the zoo said.
"Giraffes today breed very well, and when they do you have to choose and make sure the ones you keep are the ones with the best genes," Bengt Holst, the zoo's scientific director, told the BBC.
Such culling occurs 20-30 times a year at the zoo, Holst said.
The policy doesn't sit well with animal rights activists and others, the Copenhagen Post said.
"The zoo have produced him so it is their responsibility to find him a home, no matter how long it takes," Maria Evans, whose got 26,000 people to sign on to her unsuccessful online petition seeking to save the giraffe.
"They must not be allowed to take the easy option."
Stine Jensen of Denmark's Organization Against the Suffering of Animals, said the zoo rejected offers from her group and others to care for the giraffe.
"We offered to save his life," she told the BBC. "Zoos need to change the way they do business."