Police have condemned the deliberate killing of a rare monkey which was found dead north of Brisbane at the weekend.

It is believed a male and pregnant female cotton-top tamarin escaped from Alma Park Zoo when thieves broke in and tried to steal them on Saturday.

The male monkey was found the next day in a suburban backyard and tests show it had been hurled on the ground, kicked and stomped on.

Inspector Russell Miller say killing an endangered animal is a serious crime.

"They could face up to two years' jail," he said.

"There is no doubt in the world that it was deliberate - the lock on the cage was cut so someone was certainly deliberate enough to do that to the cage.

"It's just inhumane ... to do anything like that to any animal is just inexcusable."

The female monkey is still missing and the zoo's owners do not know if it is alive.