The animal, wearing a patterned shawl and propped up with the ouzo drink in its lifeless arms, was discovered in Melbourne's northeast by a passer-by.
"The kangaroo had been shot at least three times, prior to it being arranged in the chair," said Victoria state Department of Environment, Land, Water and Planning senior investigator Mike Sverns.
"This is appalling and immoral behaviour," Mr Sverns added.
In appealing for information, he warned that killing protected native wildlife was a serious offence with fines of up to Aus$36,500 (US$28,000) or 24 months' imprisonment.
Investigators suspect the animal was killed at a different location and moved to the roadside, where a passer-by made the gruesome discovery.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.