Publicist Steve Rohr, who represents Carter and her husband, actor Hal Holbrook, said Carter died on Saturday morning.
A native of Tennessee, Carter was most famous for playing quick-witted Southerner Julia Sugarbaker for seven years on Designing Women, the CBS sitcom that ran from 1986 to 1993.
She was nominated for an Emmy in 2007 for her seven-episode guest stint on the ABC hit Desperate Housewives.
Carter's other credits include roles on the series Family Law and Different Strokes.
She was married to Holbrook since 1984.