Thigpen died Wednesday night in her Los Angeles home. She had been in good health and the cause of death was not immediately known, network spokeswoman Beth Haiken said Thursday.
Production was shut down on "The District," which stars Craig T. Nelson as Washington, D.C., police Chief Jack Mannion. Thigpen played Mannion's secretary, Ella Farmer.
"I'm in shock. She was a wonderful actress and a friend," Nelson said in a statement.
"The beauty, compassion and talent that you saw on the screen was not just superb acting, it was the very essence of this wonderful woman," said John Wirth, the drama's executive producer. "We will miss her terribly."
Haiken said the 20th episode was in production this week; two more episodes were planned for the season. She said no decision had been made about how Thigpen's death would be dealt with on the show.
Thigpen, who was born and raised in Joliet, Illinois, and made her home in New York, had a distinguished stage career and also worked steadily in films and television.
In 1997, she received the Tony Award for best supporting actress for her role as a black Jewish feminist in Wendy Wasserstein's play "An American Daughter."
Thigpen re-created the role in the 2000 TV movie version of the play.
She also was nominated for a Tony for her role in "Tintypes," and won Obie Awards for "Jar the Floor" and "Boesman and Lena."
On TV, she portrayed the chief in the PBS series "Where in the World Is Carmen Sandiego?" and "Where in Time Is Carmen Sandiego?" She also appeared in the series "thirtysomething" and "L.A. Law" and the Hallmark Hall of Fame presentations of "Night Ride Home" and "The Boys Next Door."
Her film credits include "The Insider," "Shaft," "Random Hearts," "Lean on Me," "Tootsie" and the recently released "Anger Management."