Information Minister Yaacob Ibrahim on Friday ordered the books moved to the adult section, where parents can borrow them for their children, after another title had already been "pulped" by the National Library Board (NLB).
"We stand by NLB's decision to remove the three books from the children's section," Yaacob said on his Facebook page, adding that the board "will continue to ensure that books in the children's section are age-appropriate".
Singapore has separately banned a volume of the long-running US comic Archie because its depiction of a marriage between two men was deemed to breach "social norms".
Government officials insist most Singaporeans are conservative and do not accept homosexuality.
The two books to be moved to the adult section of public libraries are And Tango Makes Three - a true story about two male penguins in a New York zoo that raised a baby penguin - and The White Swan Express, which features children adopted by straight, gay, mixed-race and single parents.
The book that has already been destroyed is Who's In My Family, which discusses different types of families, including references to gay couples.
About 400 people including parents gathered at a library branch last weekend to read the banned books to their children as a show of protest.
Sex between men is illegal in Singapore and punishable by up to two years in jail.
The government's refusal to rescind the law - which is not being actively enforced - has become a lightning rod for a growing movement for gay rights in the multi-racial island nation of 5.4 million.
More than 20,000 people gathered in a peaceful rally on June 28 supporting gay rights despite a fierce online campaign against the event by conservative Muslims and Christians.
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