Fisher was taken ill on a flight from London to LA on Friday and was taken to hospital when the plane landed.
But a family statement said with “deep sadness” she died on Tuesday morning.
As well as starring in other films such as The Blues Brothers and When Harry Met Sally, Fisher also wrote four novels and three memoirs.
In a statement released on behalf of Fisher’s daughter Billie Lourd, spokesman Simon Halls said: “It is with a very deep sadness that Billie Lourd confirms that her beloved mother Carrie Fisher passed away at 8.55 this morning.
“She was loved by the world and she will be missed profoundly. Our entire family thanks you for your thoughts and prayers.” (Courtesy BBC)