Smith was reacting to Bryant being asked if his mother was a prostitute by Dolphins general manager Jeff Ireland during a predraft visit in March.
Ireland apologized to Bryant on Tuesday after a Yahoo! Sports report said Ireland asked the question.
Dolphins owner Stephen Ross said Wednesday that he will look into Ireland's interview conduct.
"Jeff Ireland has already apologized for questions asked of former Oklahoma State receiver Dez Bryant," Ross said in a statement. "I will be looking into this matter personally and will take appropriate actions if necessary."
Bill Parcells, a former Cowboys coach, who is now an executive with the Dolphins was unavailable for comment. Parcells hired Ireland.
"We need to make sure the men of this league are treated as businessmen," Smith said in a statement. "During interviews, our players and prospective players should never be subjected to discrimination or degradation stemming from the biases or misconceptions held by team personnel. NFL teams cannot have the free reign to ask questions during the interview process which can be categorized as stereotyping or which may bring a personal insult to any player as a man."
Bryant has not commented on the incident since Ireland apologized.