Cumberland City Council, which covers a population of about 240,000 people living near Parramatta, narrowly voted in May to "take immediate action to rid same-sex parents books/materials in council's library service".
The vote passed by six votes to five.
But NSW Arts Minister John Graham said banning books was a bad sign for civilisations, adding local councillors should not be engaging in censorship.
"It is up to readers to choose which book to take off the shelf," he said.
"We are examining the consequences this decision may have for the council continuing to receive library funding from the NSW government."
Mayor Lisa Lake was among the councillors who voted no, telling ABC Radio on Wednesday she vehemently disagreed with the decision.
"It's an appalling decision and I'm really deeply saddened by it," she said.
Five copies of a book titled A Focus On: Same Sex Parents have been in the council's libraries since 2019.
It forms part of a series that aims to inform children about "difficult realities" and "healthy ways for children to process and understand them".
"It wasn't a book that was hugely popular, but it was available," Ms Lake said.
"Rather than have people complain to me about the book, I'm now getting a lot of people who are disappointed with the decision and wishing us to reverse it."
The councillor who put forward the motion, former mayor Steve Christou, said the community wanted the book banned.
"I'm only representing the values of our community and what the majority of people are telling us ... we're not marginalising anyone here," he told ABC Radio.
Cumberland City Council straddles four federal electorates, where more than half of voters opposed legalising same-sex marriage during the 2017 postal survey.
They include Blaxland, where 73.9 per cent of people were against the change.
Sydney independent MP Alex Greenwich, who is gay, criticised the ban on social media.
"Library books don't cause harm, but bigots do," he posted on X.
Library books don't cause harm, but bigots do. — Alex Greenwich MP (@AlexGreenwich) pic.twitter.com/aBCqr2zqY6May 7, 2024
Cumberland local Caroline Staples said the area welcomed people of all backgrounds and beliefs and the move crossed a dangerous line.
"We're not about banning books just because someone does not like who is in them," she said.
Her petition to overturn the decision has received backing from Equality Australia ahead of a council meeting on May 15.
The advocacy group's legal director, Ghassan Kassisieh, said no one was being forced to borrow the book and people should be able to access material that reflected modern family life in Australia.
"The council seems to be clinging to some kind of backward stereotype that people in western Sydney are bigoted and can't decide for themselves what to borrow from the local library," he said.
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