Hamilton called for action to change “archaic mindsets” after footage of the interview surfaced on social media last June.
In another clip which surfaced later, Piquet used racist and homophobic language against Hamilton in a podcast interview when describing how Hamilton missed out on the 2016 championship to Nico Rosberg. Further offensive comments were made about former champions Nico and his father, Keke Rosberg.
Hamilton, who was awarded honorary Brazilian citizenship last June, is the sport's only Black driver.
The charges were brought by four human rights groups, including Brazil's National LGBT+ Alliance, which wanted Piquet to pay 10 million Brazilian Reals (£1.5million) for the alleged moral damages.
In his decision, Judge Pedro Matos de Arrudo said the amount of compensation was given “in the sense that one should not only appreciate the reparative function of civil liability but also (and perhaps mainly) the punitive function so that, as a society, we can someday be free from the pernicious acts that are racism and homophobia”.
He added: “This offense is intolerable. Even more so when one considers the projection that is given when it is a person as recognized and admired as the defendant.”
Additional reporting by Reuters.