Owners could donate a maximum of four animals, zookeepers said, which would then be euthanised before being used as food.
Aalborg Zoo is also accepting donations of horses to be fed to its animals, provided they are accompanied with the correct paperwork.
In Denmark, horse owners can receive tax deductions in some circumstances when donating animals to zoos.
Angry social media users expressed their outrage on the zoo’s Instagram page. “Shame on you”, one Instagram user wrote.
Another said: “Asking people to send healthy animals that they don’t want any more to you, so they can be slaughtered and fed to the zoo animals is one of the weirdest things I ever read”.
“Go vegan and stop supporting zoos,” wrote a third commentator, adding a green vomit emoji.
There was outrage last week when Nuremberg Zoo in Germany killed 12 healthy baboons, citing overcrowding in their enclosure, then fed them to the lions, tigers and wolves.
Gruesome spectacle for visitors
German media reported that the baboon corpses had their hands and feet removed before they were fed to the predators, in full view of visitors to the zoo.
The zoo has defended the decision, insisting it was a last resort after attempts to find other solutions to the overcrowding failed.
The furore over Aalborg Zoo is not the first time that a Danish zoo has drawn controversy for its approach to animal death and the brutality of nature.
In 2014, Marius, a male giraffe at Copenhagen Zoo, was killed by zoo authorities as his genes were too similar to other giraffes in their breeding programme.
Despite an international outcry from animal lovers, Marius was also publicly dissected “to help educate people about wildlife”.