Steve O'Donnell, NASCAR senior vice president of racing operations, said Piquet used a derogatory term while writing on social media, a violation of NASCAR's Code of Conduct, and in addition to the fine and indefinite probation will attend a sensitivity training course.
Piquet, 28, apologized after the decision.
The Sporting News reported the offensive remark was directed against racer Parker Kligerman and a photo of himself Kligerman had posted.
The online sports news organization Bleacher Report called the remark "a three-letter slur as a one-word description of Kligerman. The word is offensive to homosexuals."
Piquet is currently 12th in the nationwide Series standings, with five races left in the season.