"As far as I can see she doesn't do any advocacy for men, she spends her time picking on sexual assault survivors," Ms Bremner told SBS News on Sunday.
"To see someone like her be rewarded for mocking those people that have been sexually assaulted sends a message that sexual assault doesn't matter in this country, survivors don't matter, it's a huge slap in the face."
SBS News has contacted Ms Arndt for comment on the criticism.
Ms Arndt came to prominence in the 1970s as a sex therapist, and has written several books including the most-recently published '#MenToo'.
The 70-year-old social commentator has labelled efforts to prevent sexual assault of university students a "rape crisis scare campaign" and accused women of making up claims of domestic violence to get back at men.
Along with her work as a journalist and author, the citation for her honour notes her 2018 "Fake Rape Crisis" university speaking tour in which she campaigned against changes to consent laws.
Ms Bremner was also shocked to discover that former sex discrimination commissioner Elizabeth Broderick is one of 19 members of the Council for the Order of Australia which considers the nominations.
Sherele Moody founded the Red Heart campaign which tracks the number of women and men murdered in Australia.
"Nothing says 'gender equity' like a powerful woman with a platform laughing with a repeat male child rapist about his young female victim using her sexuality to trick him into abuse, right?" Ms Moody tweeted.
In 2018, Ms Arndt interviewed convicted paedophile Nicolaas Bester and posted it online with the title "Feminists persecute disgraced teacher".
The former Tasmanian teacher was jailed in 2011 for grooming and repeatedly raping a 15-year-old student.
He was jailed again in 2016 for producing child exploitation material after boasting online that his crimes were "awesome".
In the interview with Ms Arndt said she had spoken to many male teachers about "sexually provocative" female students.
"Sensible teachers, of course, run a mile from these girls, but the teachers are still really vulnerable because they can easily be subject to false accusations if they reject or offend the young woman in question," she said.
Arndt issued an apology in 2018 after segments were aired on 60 Minutes, saying she did not condone Bester's crimes.
“I conducted the interview not because I condone his past behaviour but because I am concerned about vigilante justice,” she wrote on her website.
“I apologise to those I have offended by the relaxed tone of the interview, particularly in the segments of the interview shown by 60 Minutes which were carefully selected to damage my reputation."
Right-wing NSW politician Mark Latham congratulated Arndt on Sunday, praising her for "trying to ensure Australian men get a fair go in the face of obsessive left-wing demonisation".
Ms Arndt said she hoped the honour would attract more volunteers to join her campaigns including trying to shut down "illegal campus kangaroo courts".
"I have no doubt my beliefs around these issues are shared by the majority of the population," Ms Arndt told The Sydney Morning Herald and The Age.
"The mainstream media has unfortunately become dominated by a particular ideological clique which is totally out of whack with what quiet Australians think about these issues, with what ordinary people think about these issues."