The women's advocacy group and charity Share the Dignity said the phrase "Shark Week" was a derogatory term for women on their period and accused the hotel of poor form.
"There are just no words Quest Palmerston," Share the Dignity posted, sharing the now-deleted original post.
"Shaming a woman for getting her period and posting pics on social media. The Post has been taken down now, but this day and age this is poor taste. #dignity4all."
The serviced apartments chain apologised for the original post in a statement on Facebook.
"We are deeply apologetic to all for the recent post and comment on the Quest Palmerston Facebook page that has been removed, this is not in line with our standards or the Quest Brand," the statement from Quest said.
"We have addressed the post with staff responsible."
But the apology didn't appease angry commentators who continued to accuse the hotel of "period-shaming" women.
We are deeply apologetic to all for the recent post and comment on the Quest Palmerston Facebook page that has been...
Posted by Quest Palmerston on Friday, 22 February 2019
"The question that still needs answering is why is there such a culture in your organisation that permits the degrading of your paid customers. Is there NO level of respect?" someone wrote.
Another person commented: "Your staff shamed a woman for something she's no control over and yet, nowhere in your 'apology' do you actually acknowledge how outdated period shaming is or the steps you'll be taking to ensure this never happens at your hotel again."
"Whoever is running this page is immature and pathetic!!!!" someone else wrote. "Who the hell takes photos of what they think is menstrual blood, and then post it on social media (sic). That's disturbing on so many levels."
"Quest apartments … You should never air your dirty laundry in public," another user posted.
The ABC reported the employee responsible for the post has been suspended and will be subjected to an internal review.
Quest Palmerston has disabled reviews and recommendations on its Facebook page.