Her publicist, Steve Rohr, said Carter died Saturday morning of complications airisng from endometrial cancer.
"This has been a terrible blow to our family," her husband, Hal Holbrook, said in a written statement. "We would appreciate everyone understanding that this is a private family tragedy."
Designing Women ran on CBS from 1986 to 1993.
Carter starred on the drama Family Law from 1999 to 2002, and appeared in seven episodes of Desperate Housewives in 2007, for which she earned an Emmy nomination. She is also well-known for her work on Broadway.
Carter is survived by Holbrook, her husband of 25 years.