The Big Yin told how tremors and lack of mobility in his left hand have meant he can’t play the instrument or the guitar.
Music-loving Connolly started out as a folk musician and was part of The Humblebums with the late singer Gerry Rafferty.
He often played the banjo during his early stand-up performances and continued to practice in private after ditching it from his stage routine.
He was diagnosed with Parkinson’s in 2013 after a doctor spotted him walking strangely at a hotel in America and advised him to get tested. He has also had successful surgery for prostate cancer.
The 72-year-old comic is next month set to embark on an epic train journey across America for a new television series and had hoped to show off his banjo skills along the way.
However, he has now admitted defeat in his battle to carry on playing but says he will sing instead.
In an interview in Canada to promote a new run of stand-up shows, he said: “I’m starting a documentary series in a month’s time following the railways around America.
“I’m going to festivals and state fairs and all that.
“I’ve been longing to do it for a long time. The only trouble is that we’re going to bluegrass festivals and I’ve got Parkinson’s Disease and it’s really affected my left hand and I can’t play the banjo or guitar anymore, but I’ll join in on the singing at least.
“It’s been a rough go between that and the cancer. I kept telling my wife that haemorrhoids couldn’t be far behind.”
Filming begins next month on Billy Connolly’s Tracks Across America, which will be screened on ITV in the new year.
The rail odyssey will see him visit 28 states and 8,000 miles of cities, coast, mountains, desert and swamp.
Last year Connolly’s wife Pamela Stephenson said her husband may have been suffering with Parkinson’s for a decade before his condition was known.
She said: “He’s probably had it for 10 years, so it’s very, very slowly progressing. There are different strains of Parkinson’s that I’m learning about.
“I’ve actually noticed his hand shaking for many, many years ... I used to think he was playing the banjo a bit too much. I think it’s been there for a long time.”
Glasgow-born Connolly chose a banjo as his luxury item when he appeared on the BBC’s Desert Island Discs.
He will perform 13 nights in cities including Toronto, Vancouver, Montreal and Calgary this October and November.