The current line up of the band were on a national tour, and had played a gig in southern NSW's Tathra on Saturday night, with Greedy Smith as front man.
They were scheduled to perform in Melbourne on Thursday.
Mental As Anything had top 10 Australian hits with 'If You Leave Me, Can I Come Too?', 'Too Many Times' and 'Live It Up'. The band's debut album featured the song 'The Nips Are Getting Bigger', which charted inside the top 20 in Australia and is still regularly played - among many other Mental As Anything songs - on radio stations around the country.
There has been an outpouring of grief from fans since Greedy's death was announced on Tuesday.
"Beyond sad to hear of the passing of Greedy Smith... Such a kind,lovely man and an enormous talent. Soundtrack to many a great party over so many years! It was a pleasure to know him. Condolences to friends and family xx Vale #ripgreedysmith" wrote comedian Wendy Harmer on Twitter.
"'Your blood is worth bottling' - the last words said to me during an interview with the one and only Greedy Smith of the Mentals... what a charming, charismatic, and much loved front man. God rest his soul. #ripgreedysmith" said music journalist Jane Gazzo.
"RIP Greedy Smith, enjoyed seeing Mental as Anything live many times. You were taken much too young," wrote fan Laraine.
