The magazine published pictures of the tragedy, where fans were crushed to death against the steel fence of Sheffield Wednesday's Hillsborough stadium, with captions that mocked the scenes of dead and grieving fans.
One caption showing people being crushed, read "Shoppers waited for the doors to open for the end-of-year sale", while another, "pitch invaders lazy", accompanied images of victims laid out on the pitch.
Emap Australia, which publishes FHM Australia, has pledged to make a donation to the families of those who died at Hillsborough. A grovelling letter of apology has been published on the magazine's website and will be published in the UK edition as well as the December Australian edition.
The letter, from editor John Bastick, said the magazine had acted without sensitivity and that it was 'truly sorry'.
FHM Australia's executive publishing director, Geoff Campbell, said the publishers apologised unreservedly for pain the pictures must cause victims' families.
In a statement, Campbell said: "We deeply regret the photograph captions published in the November issue of the Australian edition of FHM, accompanying an article about the Hillsborough disaster of 1989. The right course of action is to withdraw this edition from sale - which we will be doing. We have been in contact with the Hillsborough Family Support Group and the Hillsborough Justice Campaign to express our deep regret and sincere apologies."
Phillip Hammond, secretary and vice chairman of the Hillsborough family support group, said he was not satisfied with the magazine's apology. He said he would urge the group's board to boycott the magazine.
It would not be the first time a publication has been deserted by readers because of inappropriate coverage of Hillsborough. In 1989, The Sun blamed Liverpool fans for the disaster and the club's supporters stopped buying the paper.
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