Clark also was fined an undisclosed amount and MLS Commissioner Don Garber also ordered him to attend diversity and sensitivity training.
Clark used the offensive language during the team's match against Seattle last week.
"Major League Soccer will not tolerate this type of behavior from its players or staff at any time, under any circumstances," Garber said. "Colin Clark has expressed sincere remorse for his actions and I believe that he will learn from this incident."
Houston's next three matches are on the road against Chicago, Columbus and D.C. United.
The Houston Chronicle reported Clark had yelled at the ball boy after the youth refused to toss him a ball. Clark apologized for his comments.
"I had a chance to speak to the ball boy after the game," Clark said. "I'm sorry to everyone who I offended with that term. I intend to never use that word again in any context. There's absolutely no excuse for using that word.
"What I said doesn't represent me. It was out of character and out of line. I made a huge mistake by using those words, and I truly regret that."