Two people came across the one-metre-long reptile while walking in Heidelberg Heights about 8:30pm local time on Monday night.
It was "sitting quietly" on a footpath in the front yard of a business on Waiora Road, police said.
Officers were called to the scene, but decided to hand the case over to the experts and a reptile catcher came to help.
The catcher will look after the crocodile until staff from the Department of Environment, Land, Water and Planning can collect it, police said.