NFL rules state a player can pull another player's hair in the process of tackling such player. When Suh grabbed Barber's hair, the officials called a horse collar penalty on the play.
Barber said it was the first time in his career that a player pulled his dreadlocks.
In the last two days of practice, Barber covered up his dreadlocks. On Tuesday, he tied them up into a pony tail and had it tucked into his jersey.
Barber said he won't cover them up for Thursday's game vs. the New Orleans Saints.
Interim coach Jason Garrett sees no problem with his starting running back's hair.
"I'm fine with that," Garrett said of the hair. "I'm fine with his hair being out. It seems to be a trend in the league."
Several players, including Pittsburgh Steelers safety Troy Polamalu, have long hair that comes out of the bottom of the helmet whether the hair style is long braids, dreadlocks or it's just long like the way Green Bay Packers linebacker Clay Matthews wears his.