The Big Yin told how son Jamie, 50, had a "problem" while visiting recovering drug addicts in West Virginia as part of his ITV travel series Billy Connolly's Great American Trail.
The comedian said his eldest child, from his first marriage to Iris Pressagh, had been to Alcoholics Anonymous (AA) and Narcotics Anonymous (NA) meetings to get help.
He said: "My son has a problem and he's in AA and NA.
"He told me when he went to the detox place some kids were being let out and they were back on the stuff before they got to the railway station. It's so powerful.
"People who don’t know about it say ‘why do they take it, just say no’. ‘Just stop and you’ll be better’. Duh. It’s extraordinary."
Addressing workers and those getting treatment at the Southern West Virginia Fellowship Home, the comic added: "You do grand work.
"Anytime they speak about this stuff they talk about it like people are losers and they are dying all over the place. They never talk about this, about people pulling themselves up and getting on with it."
Connolly told viewers that 90,000 people in America had died due to opioid addiction in the last two years.
He said: "Make no mistake, this is a middle and working class crisis. The scale of addiction is industrial. There are now over a million and a half Americans addicted to medical and illegal opioids.
"The numbers are terrifying. It's a national tragedy."
Connolly, who gave up drinking 35 years ago, said he had smoked cannabis, but had no experience of harder drugs.
He said: “I know nothing about the whole drug thing. I’ve smoked a little dope but I’ve never been deeply involved in it."
Making light of his condition, he added: “I don’t shake because I’m in need of a fix, I shake because I’ve got Parkinson’s disease.”
Connolly has previously spoken of his love of going on fishing trips with Jamie, who he said worked in theatre prop departments.
The final part of his travelogue also saw Connolly return to the stage to play his beloved banjo.
He performed country music classic 'Will the Circle Be Unbroken' at the famous Grand Ole Opry in Nashville, Tennessee.
He announced his retirement from live performance last year. He said the condition had affected his movement on stage.
The Grand Ole Opry has previously played host to music legends including Johnny Cash and Dolly Parton.
Connolly was diagnosed with Parkinson's seven years ago after a doctor spotted him walking strangely through the lobby of a hotel in Los Angeles.
He moved from New York to Florida as his doctors had advised him to live in a warmer climate.
A film of the comic's final stand-up tour is being shown for one night only in cinemas on 10 October.
The Great American Trail show saw him follow the route Scottish immigrants took in the 18th century.