The Tony Award-winning writer is best known for his play "The Miracle Worker," which was about blind and deaf Helen Keller and her teacher Anne Sullivan. Gibson also adapted the work into a screenplay for the 1962 film version starring Patty Duke and Anne Bancroft for which he was nominated for an Oscar.
The Los Angeles Times said Gibson's family did not say what the cause of the playwright's Tuesday death was.
Gibson's other plays included "Two for the Seesaw," "Golda" and "Golden Boy." He also published a volume of verse called "Winter Crook" and the novel "The Cobweb."
His wife, the former Margaret Brenman, died in 2004. He is survived by his two sons, Thomas Gibson of Stockbridge, Mass., and Daniel Gibson of Cambridge, Mass., the Times said.