The children, aged between ten and 12 years old, told police that they had sneaked into an open-air compound that held eight kangaroos because they "felt like picking on" the creatures.
"The kangaroo died from blows to the head and the chest," the spokesman said.
The children also killed three of the zoo's seagulls, seriously injuring the same amount.
As the children are underage, they were sent home, and no charges will be brought against them. However, their parents may face fines in connection with animal cruelty charges.
The dead animals were discovered on Saturday. The zoo's management did not immediately call the police as the kangaroo's wounds were not immediately visible beneath its thick fur.
The zoo's remaining seven kangaroos witnessed the attack and are said to be in a state of shock. Zoo workers hope that the installation of closed-circuit cameras will protect the creatures in the future from homo sapiens.
Due to a lack of funds to provide adequate security, a crocodile and a monkey were earlier stolen from the zoo.
Nine years ago, in the same zoo, fighting dogs ripped apart eight kangaroos.