The boy Grant filmed outside as an example was also wearing sneakers and a T-shirt.
"Unfortunately, we do have a dress code," the restaurant employee told her.
But when pressed on why the white boy was in similar clothes, the staff member could not give Grant an answer.
He tried to explain it must have been because the white boy's shirt was not considered athletic.
"I have faced racism time and time again, but it's hard AF, when you have to see your child upset because he knows he's being treated different than a white child!" Grant wrote in the caption of her video posted on Instagram.
Atlas Restaurant Group, which owns Ouzo Bay where the boy was barred, said what happened was "disturbing".
"We are sickened by this incident and we sincerely apologise to Marcia Grant, her son and everyone impacted by this painful experience," they said on Twitter.
"They deserved better."
The company said two managers were no longer with the organisation and they had revised the restaurant's dress code so children under 12, who were accompanied by an adult, would not be subjected to one.
"What took place was not only disturbing, it was also eye-opening, and we are committed to learning from it and implementing real change as a result," they said.
Retired American professional basketball player Rex Chapman said the incident was "ridiculously heartbreaking".
One woman said the restaurant ought to be ashamed.
Another man said the manager had no excuse.
"The inequality was in his face and he still couldn't admit his bias," he said.
"Atlas Restaurants Groups apologised but more diversity training is not the answer. Better staff choices is."
