The Scottish comedian and actor started out as a folk singer before developing his stand-up act.
The 72-year-old 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.
In an interview in Canada to promote his stand-up tour, 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 any more, 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."
Connolly disclosed in 2013 that he had been diagnosed with Parkinson's and prostate cancer on the same day.
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.
Billy Connolly has been forced to give up playing the banjo and guitar because of Parkinson's Disease.