She was 94.
A close friend told the daily that Rutherford died on Monday night at her home in Beverly Hills after years of heart problems and declining health.
Her role as Carreen O'Hara in the 1939 movie classic was a small one but the flick became a classic and Rutherford was one of the longest surviving cast members.
"That 'nothing part' turned my golden years into platinum," the Times quoted her as having once said.
Rutherford also appeared in westerns and as Mickey Rooney's teenage girlfriend in the Andy Hardy film series from 1937 to 1958, and on The Bob Newhart Show on television.
She was twice married, to department store heir David May II and to William Dozier who produced the 1960s Adam West Batman television series.
She is survived by a daughter and two grandsons.