In an online video compilation of NBA players sending seasonal greetings to fans celebrating Chinese New Year, Redick appears to refer to "chink" fans.
"I just want to wish all of the NBA chink fans in China, a very happy Chinese New Year," the 33-year-old says.
Redick responded to the controversy on Twitter early Sunday, blaming a verbal slip for his use of the word.
"Just saw a video that is being circulated of me wishing a happy new year to NBA fans in China," Redick wrote.
"Clearly I was tongue tied, as the word I purportedly said is not in my vocabulary. I'm disappointed that anyone would think I would use that word.
"I love and respect our friends in China."