"(It) ensures education in accordance with the values based on Hungary's constitutional identity and Christian culture."
Hungary’s constitution was rewritten soon after Prime Minister Viktor Orban came to power in 2010.
The existing document already defines "the institution of marriage as between a man and a woman" as well as "the basis of the family and national survival".
The latest proposed amendment, the ninth since 2012, comes as anti-gay sentiment over the decade of rule by Mr Orban's right-wing government escalated this year.
In September, a book of children's fairytales containing some homosexual characters was publicly shredded by a far-right politician.
"Leave our children alone," said Mr Orban during a radio interview, after calling the book a "provocative act".
In May, a ban on legally changing one's gender came into force, making it impossible for transgender people to have their official documents contain their gender and name in accordance with their gender identity.
Rights groups say this exposes trans people to potential discrimination in employment, housing, and accessing services and official procedures.
Mr Orban's anti-immigration and conservative social policies have also included a 2018 decree effectively banning universities from teaching gender studies courses.
Some of Mr Orban's critics accuse him of attacking the LGBTQI+ community in the same way he has attacked migration and migrants, as well as minority groups like the ethnic-Roma, Hungary's largest.