Harden's mother, Monja Willis, recently told TMZ that Barnes apologized for the profane remark when asked by Harden's brother to do so.
The incident occurred during the Clippers' Game 2 loss to Houston, which evened the series at 1–1.
According to ESPN.com, the Rockets informed the NBA about Barnes arguing with Houston fans during both games at the Toyota Center.
Barnes was fined $25,000 earlier this year for comments directed toward Phoenix Suns fans.
Game 3 between the Clippers and Rockets is on Friday in Los Angeles. Barnes scored a combined 26 points in the first two games of the series.
- Molly Geary