Gordon directed the term at Timbers captain Will Johnson, who held up three fingers and mouthed the words "three games" at Gordon in the immediate aftermath of the incident. The punishment is the same that was handed to Colin Clark and Marc Burch for similar actions a season ago.
"Major League Soccer stands against discrimination and prejudice of any kind and will not tolerate this type of behavior," MLS commissioner Don Garber said in a league statement. "All of our players, staff and fans must remain committed to respect and dignity at all times."
In addition to the ban, Gordon, who issued an apology after the game on San Jose's official website, was fined an undisclosed amount and was mandated to participate in diversity and sensitivity training.
"I sincerely apologize for what I said in our game tonight," Gordon wrote. "Although I said it in the heat of the moment, that language has no place in our game. That is not my character, but there is still no excuse for saying what I said. I made a mistake and I accept full responsibility for my actions."
He was publicly reprimanded by Earthquakes' president Dave Kaval, who was outspoken against his actions.
"We are working hand in hand with the league right now on this very serious matter," Kaval wrote in a statement. "Alan's comments do not reflect the views or beliefs of our organization. We have always promoted an atmosphere of acceptance and equality in our stadium and amongst our diverse and passionate fans.
"I am appalled by the use of the hurtful language on the pitch last night. We will use the collective energy and resources of our club to foster an inclusive environment for all of our fans. I hope to use this deplorable incident as a tool to help eradicate offensive language of this kind.
"For our fans, I know the organization has let you down. I will do my best to take the necessary actions to make sure we once again can be viewed as a beacon of diversity, community, and equality."
Gordon, who was red carded for a separate foul in the match, will miss a total of four games as a result of the ban: San Jose's upcoming clashes with Portland, Chivas USA, Montreal and Toronto. He will be eligible to return May 11 in the Earthquakes' match at the Seattle Sounders.