Amazed residents called the police and two officers seized the flightless bird before it could wander into rush-hour traffic in Barnstaple.
They held the animal – originally a native of Australia rather than south-west England – in the back of their patrol car for half anhour before an animal ambulance arrived and took it away.
Officers are searching for the owner of the bird.
Acting Sergeant Zoe Parnell said she had just begun her shift at 7am on Wednesday when she got a call that an ostrich was on the loose in Riddell Avenue, a residential street in the town.
"I thought it was a wind-up," she said. "I thought we'd arrive and it would be a turkey or something like that." She rushed to the scene, where she was joined by police community support officer Stephen Huxtable.
Parnell said she wasn't sure what the creature was but knew that they had to stop it reaching the main road, where the bird could have caused rush-hour chaos.
"It was trying to get into people's houses. Obviously it was finding that difficult, and would try the next one. I must admit that while I'm not normally scared of birds, I was a bit nervous with this one."
It fell to Huxtable to seize the bird and put it in the back of the police car.
Like many others apprehended by the police, the emu was not happy. "There was a lot of wee-ing and poo-ing and flying feathers in the back of the car," said Parnell. "It's going to have to be specially cleaned."
She thought about giving the bird a drink from her water container "but it was a bit distressed so I thought it was better to leave it", she said.
Instead, the officers called for backup from Diana Lewis, north Devon's "animal angel" and a leading light in North Devon Animal Ambulance.
The emu remains in her care while the search for the owner continues.The Department for Environment, Food and Rural Affairs said it was not necessary to have a licence to keep an emu.
However, Wendy Higgins of the Humane Society International/UK flagged up concerns: "In Britain, we keep more exotic wild pets than cats or dogs, and often residents can be completely unaware they are living next door to a python or a primate. Often it is only when an escape or an accident occurs that their existence is revealed.
"Unbelievably, there is no definitive national register of the number and variety of exotic animals being kept in the UK or traded globally.
"Wild and exotic animals are not pets, but a welfare disaster waiting to happen. It is high time the appalling commerce in wild animals for the pet trade was brought under serious control and preferably banned altogether."
Emus used to fall under the Dangerous Wild Animals Act 1976 but have been delisted.
Higgins said: "However, the list of species covered has been seriously reduced, many local authorities fail to effectively enforce he legislation, and there are serious questions regarding the competence of those that do. As a result, non-compliance levels are believed to be high."
*Barnstaple is not far from the headquarters of the CFZ UK - If they never find the owner, perhaps Jon Downes could take it in!