The 72-year-old Scottish star started out as a folk singer before developing his stand-up act. Connolly often travelled with his banjo but now says he can no longer play as he prepares to travel across the US by rail for a new TV series.
Connolly said Parkinson's had particularly affected the use of his left hand.
When he was on Desert Island Discs, Connolly chose a banjo as his luxury item and he also has a banjo tattoo on his left hand.
"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 any more, but I'll join in on the singing at least.
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"It's been a rough go between that and the cancer. I kept telling my wife that haemorrhoids couldn't be far behind."
He has since been given the all-clear from cancer and will travel through 28 states and 8,000 miles by train later this year in new ITV documentary series "Billy Connolly's Tracks Across America".