"This has been a terrible blow to our family," her husband, actor Hal Holbrook, said in a statement. "We would appreciate everyone understanding that this is a private family tragedy."
Carter died from complications arising from endometrial cancer, publicist Steve Rohr tells PEOPLE.
Best known for her role as interior designer Julia Sugarbaker in Designing Women, the Tennessee native earned an Emmy nomination in 2007 for her guest appearance on Desperate Housewives.
Her Broadway credits include a stint in Thoroughly Modern Millie in 2004.
Carter and Holbrook, who married in 1984, appeared together last year in That Evening Sun, an independent film based on a short story by author William Gay.
In addition to her husband, Carter is survived by two daughters from a previous marriage.