Traffic controllers monitored the wallaby as it bounded off the bridge onto an expressway and made its way to a city centre street, where several police officers cornered it.
Farr-Jones was among early-morning drivers who spotted the marsupial as it hopped down the busy road just before 5am on Tuesday.
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Police said they chased the animal over the bridge before dawn.
"It's unprecedented to try and get a hold of a wallaby on the Harbour Bridge".
Veterinarian Larry Vogelnest said the wallaby was "quite distressed" but he gave it a tranquilizer before taking it to the wildlife hospital at nearby Taronga Zoo.
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He was given pain medication and fluids and is in Taronga's Wildlife Intensive Care Unit for recovery and further monitoring before being returned to the wild.
'In the past few decades. we have seen swamp wallabies slowly spreading back into suburbia, especially in Sydney's leafy north, ' he said.
"These animals are quite susceptible to stress, and it causes muscle damage so I don't know whether that's happening", he said.
However the wallabies are becoming more common around Sydney, Harris and Dr Vogelenest both said, due to rapid development of Sydney's suburbs.
"It's unusual obviously to have a wallaby running around on the Harbor Bridge, but there are more and more of these wallabies turning up in bush land close to the city", Vogelnest said.
It was initially believed the wallaby might have come from the near the Cammeray Golf Course, but greenskeepers said they had never seen wallabies on the course.