Christie Whelan Browne, Erika Heynatz and Angela Scundi have accused the 52-year-old of inappropriate touching and harassment during the 2014 stage production of the Rocky Horror Show.
Victoria Police confirmed it is investigating two allegations.
McLachlan has now stood aside from his role in the 2018 stage production of the cult film, which opened in Adelaide on New Year's Eve.
The claims, which were published by the Australian Broadcasting Corporation (ABC) on Monday, include allegations that McLachlan inappropriately kissed Whelan Browne's bottom, kissed Heynatz without her permission and exposed himself to Scundi.
They also allege he bullied and intimidated some cast members.
McLachlan, 52, who is in a long-term relationship with conductor Vanessa Scammell, rejected the allegations as "entirely false", and questioned the women's motivation for coming forward.
"Frankly, they seem to be simple inventions, perhaps made for financial reasons, perhaps to gain notoriety. In either event, they are to the best of my knowledge utterly and entirely false," he said in an email to ABC.
The women say they have come forward to protect current cast members from risk.
McLachlan first played the raunchy role of Frank N Furter in 1993, then reprised his role in 2013 and 2014.
The producer of the show, The Gordon Frost Organisation, issued a statement saying it was "shocked" to learn of the allegations which it took "very seriously".
It said it had spoken to McLachlan and "mutually agreed that it is not appropriate for him to continue in the current production of the show".
It insisted it was previously unaware of the allegations, saying "records show the claimants at no time made any complaint - formal or informal - to the company manager or executive producer of The Rocky Horror Show in 2014".
Two of the women said they complained to a senior member of staff at the time of the alleged harassment, but nothing was done.
The production company says a full internal investigation will now take place.
Production of Australian TV series The Doctor Blake Mysteries, in which McLachlan plays the lead role, has been put on hold pending the police investigation.
McLachlan shot to fame in Australian soap Neighbours, playing Henry Ramsay - the brother of Charlene, played by Kylie Minogue.
After winning Australia's top television award - the Gold Logie - he went on to achieve pop success, reaching number 2 in the UK Singles Chart in 1990 with Bo Diddley cover Mona.