The note King wrote in April, 1960 went on sale on Tuesday (25Mar14) on website MomentsInTime.com for $125,000 (£78,000).
It is believed to be the only letter King wrote to Parks. In it, he responds to a letter he received from her in March, 1960.
It reads in part: "In the midst of constant harassment and intimidation because of my involvement in the civil rights struggle I often find myself asking, 'Is it worth it?' But then a friend of good will come along with kind and encouraging words that gives me renewed vigor and courage to carry on. Your letter serves such a purpose."
Parks became a civil rights figure in 1955 when she was arrested for refusing to give up her seat on a city bus to a white passenger in Montgomery, Alabama.