Australians often joke that tourists expect to see kangaroos hopping across the Sydney Harbour Bridge but the joke was on police on Tuesday when a wayward wallaby led them in an early-morning chase across the famous landmark.

Police said they chased the mysterious marsupial on foot and in a car over the bridge before dawn before catching it in a downtown park and taking it to the city's Taronga Zoo.

"Officers took the startled macropod into police custody ... with the police mounted unit arriving on scene soon after to take it to the zoo for veterinary assessment," New South Wales Police said in a statement.