The school's principal quit after a complaint about a sixth-grade art class that included an image of the statue.
A parent had complained the image was pornographic.
Cecilie Hollberg, director of Galleria dell'Accademia, has now issued the invitation to the class.
She said the principal should be "rewarded, not punished".
"Talking about the Renaissance without showing the David, an undisputed icon of art and culture and of that historical period, would make no sense," Ms Hollberg said.
The controversy began when the board of Tallahassee Classical School - a charter school in Florida's state capital - pressured principal Hope Carrasquilla to resign after three parents complained about a lesson that included a photo of the 17ft nude marble statue.