The band originally formed in 1977 in Perth, Australia and have sold 30m albums worldwide, with six UK Top 10 albums and five US Top 20 albums.
Perth Now reports that drummer Jon Farriss announced at a hometown gig that the band would be disbanding after the show, making it the group's last performance together.
After the performance, lead singer Ciaran Gribbin wrote on his Facebook page: "Dear friends, I know a lot of you are concerned and want clarification on what happened at the INXS gig last night in Perth. As I write this most of INXS are on a plane flying from Perth to Sydney.
"Please try and be patient as the Band plan to release a full statement on the subject ASAP. I'm sorry I can't say anymore at this time and hope this helps ease a few worries and concerns."
The band are expected to release a full statement on Tuesday.
INXS achieved huge success in the late 1980s and early 1990s with the release of their album Kick and hit singles such as 'Need You Tonight', 'New Sensation', 'Never Tear Us Apart' and 'Suicide Blonde'.
After the death of Michael Hutchence in 1998, the band replaced him with Jon Stevens, then JD Fortune, and finally Ciaran Gribbin last year.
The news comes as a shock to many, as keyboardist and founder member Andrew Farriss had told Billboard last month that the band had been working on new material: "I've got maybe four, five new tracks I'm happy with, and there's a lot of other material.
"Because we're out touring, it's a little bit frustrating because I want to stop and concentrate on that (new) work. But you've got to be patient and make sure it's right. But this particularly lineup of INXS is really - we're on a winner, I think, with this one. It's looking really, really positive."
Watch INXS's video for 'Need You Tonight' below: