In a sad twist, Spencer's character on the popular NBC show had also suffered a heart attack that forced him to leave his job at the White House.
Spencer, 58, died in a Los Angeles hospital on Friday, said his publicist Ron Hofmann.
"We're shocked and deeply saddened by the sudden death of our friend and colleague," said a joint statement from the creator of the series, Aaron Sorkin, and one of the original executive producers, Tommy Schlamme.
Actor John Spencer displays his Emmy for outstanding supporting actor in a drama series for his work in The West Wing. (AP photo)
"John was an uncommonly good man, an exceptional role model and a brilliant actor. We feel privileged to have known him and worked with him. He'll be missed and remembered every day by his many, many friends."
NBC said it didn't know what effect Spencer's death would have on The West Wing, which is in production on its seventh season.
Spencer, who had scores of film, television and stage credits, began his TV career as an actor in the 1960s sitcom The Patty Duke Show.
He played New York lawyer Tommy Mullaney in L.A. Law in the 1990s.
He won an Emmy Award for supporting actor in 2002 for his work in The West Wing.
