Terry was acquitted of abusing Ferdinand by Westminster Magistrates' Court in July, but the FA's disciplinary committee announced that the 31-year-old was guilty of abusing Ferdinand on the balance of probabilities, rather than beyond reasonable doubt.
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The Blues star announced his retirement from international football with England on the eve of his FA hearing after stating that the governing body had made his position within the side untenable by pursuing the case against him.
Terry will have 14 days after receipt of the written reasons for the decision to launch an appeal, and the penalty is suspended until after the appeal should the Chelsea captain decide to do so.
The decision means that Terry will be free to represent the club in their London derby against Arsenal at the weekend, and for up to two weeks afterwards if he does appeal.
Terry's management company have released a statement, saying that: "Mr. Terry is disappointed that the FA Regulatory Commission has reached a different conclusion to the clear not guilty verdict of a court of law.
"He has asked for the detailed written reasons of the decision and will consider them carefully before deciding whether to lodge an appeal."
Terry is the second Premier League player in under a year to receive a ban and fine after being found guilty of racism following Luis Suarez's eight-game sanction and £40,000 fine for abusing Manchester United defender Patrice Evra.
Chelsea released a statement that affirmed their respect for the FA ruling, and also for Terry's right to appeal, and therefore said that it was inappropriate to make any further comment.