A wallaby hopping along the Sydney Harbour Bridge has surprised motorists early this morning, with police later cornering the startled animal and taking it to a vet for a check-up.

Callers to Sydney radio station 2GB witnessed the marsupial jumping about the lanes on the northern side of the bridge just before 5:00am.

"I couldn't believe what I was seeing," one caller, Michelle, said .

"I was so worried about the poor little thing. It was just hopping northbound in lane eight.

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"I thought 'No, no way do you see a kangaroo in the city like that," she said.

"I've only seen them in the country."

Traffic controllers from the Transport Management Centre, including Dave Wright, monitored the wallaby.

"Traffic controllers had quite a surprise early this morning when we saw a kangaroo making its way down lane number eight of the Sydney Harbour Bridge coming from the northside," he said.

"It basically continued to hop, making its way from lane eight all the way over to lane one … down the Cahill Expressway and down to Macquarie Street," he said.

Motorists called police, and officers from Harbourside and North Shore local area commands responded.

"There was a police car following it at a really slow pace and there were a lot of cars behind it," another 2GB caller, Dean, said.

"It was just just hopping down the street. I've never seen anything like it. That's Australia for you."

Police were able to corner the wallaby near the Conservatorium of Music. ( Twitter: Sunrise )

"It was on the Cahill Expressway on top of Circular Quay," a third 2GB caller, Ray, said.

"It was just standing there minding its own business with a police car there with flashing lights and everything."

Police were later able to pin down the out-of-place animal.

"Officers took the startled macropod into police custody near the Conservatorium of Music, with the Police Mounted Unit arriving on scene soon after to take it to the zoo for veterinary assessment," police said.

Animal stressed but free of major injuries

The male adult swamp wallaby was taken to The Taronga Wildlife Hospital in Sydney where it was assessed by senior veterinarian Larry Vogelnest.

"It was quite distressed … so I elected at that point to anaesthetise it … to give it an injection so it was asleep because it was very stressed," he said.

"Then I examined it thoroughly. Fortunately there didn't seem to be any significant injuries.

"It had some minor grazes on its face and its hind legs.

"I X-rayed its whole body to rule out any fractures … and there didn't seem to be any major injuries."

The wallaby is recovering and is expected to be released into bushland. ( Supplied: Taronga Zoo )

The wallaby will be monitored at the hospital's intensive care unit for the next 24-hours and later released in bushland where there were other swamp wallabies.

Police Inspector Kylie Smith said it was an extremely uncommon call-out for police.

"It was a very unusual job for a city police officer to be chasing a wallaby down the Harbour Bridge," Inspector Smith said.

The wallaby was likely taking in the famous sights she joked.

"Sydney's got the best harbour in the world so I'd imagine he was taking in the view."

Asked about the global media coverage the story has received, Inspector Smith said "what a beautiful harbour Sydney has".

"So, wake-up all across the world and know that we actually do have wallabies or kangaroos that jump down the main street of Sydney."

It was thought the wayward wallaby might have made its way to the bridge from a golf course in Cammeray, police said.

Ollie Gebert is a junior golf instructor and was at the nine-hole Cammeray golf course this morning but has never spotted a wallaby there.

"I've never seen one in 25 years. There is a lot of bushland over at Northbridge and the back of Cammeray so maybe it's come from there," he said.

The wallaby may have used the golf course to access the freeway that leads to the bridge, he said.

"Obviously it's a big possibility. This is the only entry. At the back of the golf course near the 6th hole there's an entry to the freeway so that's the only way I can see it jumping on from the golf course."