Humberside Police said they are investigating the death of the marsupial, which was kept at the centre in East Park.
A spokesman said today that the wallaby was found to be unwell on February 23.
She had to be put down by a vet and her joey also died, the spokesman said.
"A post-mortem examination found an air pellet in the animal's skull which caused its death," he said.
"The pellet is thought to have been there for over a week."
The force said it has begun an investigation into offences under the Animal Welfare Act 2006 (animal cruelty) as well as offences of trespass and criminal damage.
It is thought that an intruder broke into East Park overnight some time between February 10 and February 20, and then shot the wallaby while she was in her pen.
Anyone with information is asked to call If you know anything that would help us please call 101 quoting log 227 05/03/18.