The 69-year-old Brazilian, who won the world title in 1981, 1983 and 1987, used a racially offensive term when referring to Hamilton on a Brazilian podcast.
“Discriminatory or racist language is unacceptable in any form and has no part in society,” Formula One said in a statement.
“Lewis is an incredible ambassador for our sport and deserves respect.
“His tireless efforts to increase diversity and inclusion are a lesson to many and something we are committed to at F1.”
Motorsport’s governing body the FIA also spoke out in “solidarity” with Hamilton.
“The FIA strongly condemns any racist or discriminatory language and behaviour, which have no place in sport or wider society,” the FIA said in a statement.
“We express our solidarity with Lewis Hamilton and fully support his commitment to equality, diversity and inclusion in motor sport.”
Piquet was discussing an accident between Hamilton and Red Bull’s Max Verstappen on the first lap of last year’s British Grand Prix when he used the term.
His daughter, Kelly, is Verstappen’s partner.
Hamilton, the only black driver on the grid, has been an outspoken campaigner for greater diversity in the sport.
The seven-time world champion regularly displayed “black lives matter” on his apparel and took the knee before races in the 2020 season following the murder of George Floyd in the USA.
“We condemn in the strongest terms any use of racist or discriminatory language of any kind,” Mercedes, Hamilton’s team, said in a statement.
“Lewis has spearheaded our sport’s efforts to combat racism, and he is a true champion of diversity on and off track.
“Together, we share a vision for a diverse and inclusive motorsport, and this incident underlines the fundamental importance of continuing to strive for a brighter future.”
Hamilton is back in action on home soil this weekend for the British Grand Prix at Silverstone.