The Nationwide Series driver posted the remark on Instagram Sept. 25 in a post that has since been deleted.
"Nelson Piquet Jr. recently communicated an offensive and derogatory term that cannot be tolerated in our sport," said Steve O'Donnell, NASCAR senior vice president of racing operations. O'Donnell added the 2013 code of conduct clearly defines NASCAR's position "regarding the use of disparaging terms. We expect our entire industry to abide by this Code."
Piquet apologized in a statement.
"I sincerely apologize to everyone for my poor choice of words last week. I did not mean to hurt or offend anyone," the Brazilian said in a statement.
"This has been a cultural learning experience that will make me a more sensitive person moving forward."
Turner Scott Motorsports said in a statement it had addressed the issue with Piquet, who understood the team does not tolerate such remarks.
"TSM expects those associated with the team to uphold professional standards that we can all be proud of," TSM said in a statement. "Nelson has assured the team that he has learned his lesson and he knows what it means to represent TSM."
Earlier this year, NASCAR suspended Nationwide Series driver Jeremy Clements for two weeks for using a racial slur. Clements made the remark to a blogger for MTV News during an interview at Daytona.
Meanwhile, NASCAR also on Tuesday penalized Penske Racing because Joey Logano's race-winning Nationwide car at Dover failed post-race inspection on Saturday.
Crew chief Jeremy Bullins was fined $10,000 and team owner Roger Penske docked six championship car owner points because the front of the car was too low.
Penske Racing said in a statement the car failed inspection because a spring retaining screw came unscrewed.
"The problem is being addressed internally to prevent it from happening again and the team is not planning to appeal the penalty," the statement said.