EBONY the rabbit and Piggy the guinea pig were furry companions to Melbourne kindergarten children for two years.

That was before Ebony was decapitated and Piggy died of shock in what police called a disgusting attack.

Police said someone pushed rubbish bins together to climb the three-metre-high wall of the Smith Street Early Learning Centre in Thornbury at midnight on Monday.

After setting Ebony and Piggy free, they decapitated the rabbit and the guinea pig died of shock.

Kindergarten staff found the grisly remains buried in the vegetable garden and the playground before children arrived on Tuesday.

The children have created a memorial wall to say goodbye to their fuzzy friends.

Senior Constable Marcia Fabris asked the public to look out for people boasting on Facebook or other parts of the internet about the attack.

"I think this is a disgusting, disgraceful crime," Sen Const Fabris told reporters on Wednesday.

"I can't believe someone would do this to children's pets."

Sen Const Fabris said police did not know if more than one person was involved.

She appealed for anyone with information about the attack to contact police.