Families, activists and political opponents are to protest against the ban in Milan on Saturday.
Ms Meloni, who leads the far-right Brothers of Italy party, made anti-LGBT rhetoric a cornerstone of her electoral campaign, promising to protect traditional values.
Ahead of her election victory, Giorgia Meloni campaigned against what she termed "gender ideology" and the "LGBT lobby"
"We were always a family, but being officially recognised as such by our own mayor made us feel welcome," said Maria Silvia Fiengo. "Today, looking at what the government is doing, and knowing that other families won't be able to have the same opportunity, we feel discouraged."