Farnsworth's fiancee, Jewely Van Valin, said that he himself was struggling with pain caused by cancer as he made the film.
He was 80, and had been diagnosed as suffering from terminal cancer.
Tom Sullivan, the Sheriff of Lincoln county, where Farnsworth lived, said: "This was an obvious self-inflicted gunshot."
Farnsworth spent 40 years as a stuntman and double before winning his first speaking role at the age of 57. His career peaked this year with an Oscar nomination as best leading actor for his role in Straight Story.
In pain
In the film he played an elderly man, Alvin Straight, who drove from Iowa to Wisconsin on a lawn mower to see his brother, who was dying of cancer.
Farnsworth's fiancee, Jewely Van Valin, said that he himself was struggling with pain caused by cancer as he made the film.
Farnsworth was the oldest leading actor ever to be nominated for an Oscar.
He had earlier received a nomination as best supporting actor in his portrayal of a wagon driver in the 1978 film Comes a Horseman.
Sheriff Sullivan said Farnsworth was found dead at the home he shared with Ms Van Valin.
"She called a neighbour who was one of my former deputies... He went over and found Mr Farnsworth."
Supporting roles
Farnsworth was born on 1 September 1920 in Los Angeles and began his career as a stuntman at the age of 16, often doubling for stars in Westerns.
"If there was a wagon or something I would be driving it," he was quoted as saying.
"But they didn't let me say anything."
His first speaking role was in The Duchess and Dirtwater Fox in 1976. He also appeared in The Grey Fox, The Natural, Tom Horn, Resurrection, Rhinestone Cowboy, Anne of Green Gables, Havana and Misery.
Farnsworth's weathered face and crystal blue eyes were easily recognisable.
Ms Van Valin said he would be buried in Hollywood.