"In the last few days we saw that the baby chimp had been treated very roughly by two of the younger males in the group, without the mother stepping in," Aalborg Zoo said. "Last night we sedated the baby and established that it was so weakened and injured that it would not survive."
The zoo told The Copenhagen Post that the baby's mother, Laura, had not displayed interest in defending her offspring.
Zoo representatives said the only other option was to remove the baby from the group and bottle feed it.
"If we'd done that we'd have wound up with a chimp that was influenced by humans and that could never be reintroduced to the group again, which is not something we want."
The chimp was Laura's fourth baby, the first two of which were stillborn.
Less than a month ago, a polar bear at the zoo had to be put down after breaking his front legs following a fall into a deep security pit that surrounded his enclosure.