Deputies said the barber fixed the haircut for free, according to KHOU. The argument broke out in the parking lot of the shop, the television station reported.
Deputies said the father shot the barber three times before fleeing in what could be a four-door, gray sedan, KPRC reported.
The barber is listed in stable condition, the television station reported.
"I think it's just crazy for anyone to shoot anybody over a haircut, period," Detective Wallace Wyatt told KHOU. "The disturbing part is his 13-year-old son witnessed this, which makes him a part of this, so this 13-year-old son knows he needs to come forward and tell us what happened. The father knows he needs to come forward and tell us what happened. Just to be an example, to be a good father and say, 'I messed up. I have something to prove to my son, and this is how you fix it.'"