"Andrew is survived by his son Harvey, fiancée Fiona Docker and brother Stuart."
Smith — who wrote many of Mental As Anything's hit songs, including Live It Up — had been with the band since it formed in the late 1970s.
Reg Mombassa, Martin Plaza, Wayne De Lisle and Peter O'Doherty were the other founding members, though only Smith was still performing with the live band.
In addition to songwriting, he played the keyboard and was the band's co-lead singer.
Smith also released two solo albums: Love Harmonica in 1996 and Greedy's People the following year.
Fans have been paying tribute to the musician on social media, with Shelley Stocken — who worked with Smith on his 1996 solo album — writing: "I don't recall working with a kinder, more giving or more cheerful artist before or since. What a loss!"
Others reminisced about what the band meant to them while lamenting Smith's loss:
