The video, filmed by Greg Bloom, shows the kangaroo release the dog and turn its attention to Tonkins, who punches the marsupial in the face before fleeing with his canine.
The kangaroo appears stunned but uninjured.
Mathew Amor, who organized the hunting trip in June, said the footage was filmed for a DVD being recorded for a hunting party member named Kailem, who was suffering from terminal cancer and wanted to go on a last boar hunting trip in Condobolin, New South Wales.
"This hunting trip was put together for a sick young man called Kailem who passed away from cancer last week," Amor told News.com.au.
Amor said the kangaroo seemed surprised by the punch, but was not hurt.
"My mate only stunned it," Amor said. "His hand was OK, he didn't hit it very hard at all. It was funny because the guy who did it is the most placid bloke. We laughed at him for chucking such a [expletive] punch."
The Taronga Western Plains Zoo confirmed Tonkins is an employee.
"Good animal welfare and the protection of Australian wildlife are of the utmost importance to Taronga," the zoo said."We are working with Mr. Tonkins to understand the exact circumstances of the event and will consider any appropriate action."