As the Sounders beat Real Salt Lake in the Western Conference semi-final playoff on Thursday, Burch was heard making a remark which has now been deemed as unsavoury by the league and he has been punished for his misdemeanour.
Burch issued a statement of apology but has still received the playing ban as well has ordered to pay an undisclosed fine and instructed to attend sensitivity training.
"Major League Soccer has a zero tolerance policy in response to this type of behavior from its players or staff," said MLS commissioner Don Garber in a news release.
"While I understand and believe that Mr. Burch is remorseful, Major League Soccer is committed to providing an environment in which all individuals are treated with dignity and respect."
Burch missed Sunday's 3-0 loss to the LA Galaxy and is also unavailable for the return leg next week. His third match will be served in the MLS Final if Seattle overcome their deficit or in the season opener of the 2013 campaign.