The 1979 Black Ludwig touring and recording kit is part of just the second exhibition held at the museum in Melbourne.
ENCORE! shows off 50 years of Australia's performing arts history through a display of 50 objects, with the drum kit one of the standouts.
Hirst died in January at the age of 70, and was the principal songwriter of many of Midnight Oil's biggest hits, including Power and the Passion and Beds Are Burning.
He played the kit onstage for Midnight Oil shows from 1979 up until the band's farewell concerts in 2022.
It's on public display for the first time since it was donated to the museum by a fan group, which crowdfunded its purchase at auction for $77,500.
The fans had reportedly made inquiries with the Powerhouse in Sydney, the band's home town, however the institution did not respond.
The ENCORE! display also includes items such as Kylie Minogue's gold hotpants from the Spinning Around music video, plus the Ossie Ostrich puppet from Hey Hey It's Saturday.
There's also a gown worn by the late Olivia Newton-John while performing with ABBA, and a set model of the Priscilla, Queen of the Desert bus.
The items are drawn from a collection of more than 875,000 objects from circus, dance, music, opera and theatre held by the Australian Performing Arts Collection, and the exhibition marks the collection's 50th anniversary.
The museum opened in December 2025 and its inaugural show DIVA, from London's Victoria and Albert Museum, pulled in an audience of more than 39,300 people.
The ENCORE! display will be on show from Wednesday until May 2027.
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