The woman, an English teacher at the Marco Polo high school in central Venice, had shared online articles about migrant rescues with comments such as: "Another rescue... can't we let them die?"
She called the influx of migrants to the country as an "invasion" and "the plague of the third millennium" and referred to Muslim children as "future criminals, to be eradicated", according to local paper Venezia Today.
The teacher's Facebook page has now been taken down, but Italian media have shared screenshots of the offending statuses.
In several posts, she wished death on refugees, saying: "I hope they all drown... that no-one is saved" and "burn them alive".
Two deputies from the Italian Left party, Giulio Marcon and Celeste Costantino, have called for an "urgent investigation" into the high school by the Ministry of Education, to confirm if the teacher is responsible for the posts and whether she should face disciplinary action.
Macron used his own Facebook page to condemn the teacher's actions, asking: "What is a teacher who incites hatred teaching children?"
The woman, a 59-year-old, also used social media to praise former Italian fascist leader Benito Mussolini and to criticize several prominent Italian politicians.
In particular, she targeted Prime Minister Matteo Renzi, President of the Chamber of Deputies Laura Boldrini (whom she called a "disgusting whore, bitch") and Venice's mayor.
In their formal request to the Ministry of Education, Marcon and Costantino described the xenophobic comments as "absolutely horrific".
They said that while "thousands" of social media profiles shared similar posts, such views were unacceptable coming from "the public profile of a teacher at one of the most important schools in Venice's historic centre, where there is a growing number of foreign and Muslim children".
Around 1,000 children ages 14 to 19 study at her school, and the two deputies noted that "of course" many of them would be familiar with their teacher's posts.