Orthopaedic surgeon Gary Fettke, from Tasmania, met Connolly in a Los Angeles hotel lobby and revealed to the comedian the possibility he may have Parkinson's.
The surgeon had approached the Glasgow comedian to ask for an autograph but, after watching the way the 71-year-old was walking, he decided to tell him that he was showing early signs of Parkinson's.
Dr Fettke was in the Sportsmen's Lodge in Los Angeles, in January 2013, with his daughters' dance troupe when he saw Connolly across the lobby.
They started talking after one of the girls asked Connolly for his autograph.
As he was walking away Dr Fettke noticed that Connolly had a "strange gait".
Dr Fettke's wife, Belinda, said: "He was such a nice guy and spoke to us for quite a while about Tasmania and the girls and his tour.
"As he walked away Gary said to me he was sure Billy had Parkinson's."
Dr Fettke said Connolly walked the same way as someone who had been drinking.
Dr Fettke said: "I thought maybe he didn't realise he had it. It was just one human being to another human being, who happened to be Billy Connolly."
Later on the night of the encounter, the keen-eyed surgeon searched online and found no reference to Connolly having Parkinson's.
The next morning Dr Fettke met Connolly again and told him he wanted to catch up for a quiet word.
He told Connolly he was his biggest fan before he delivered the bad news.
He said: "I told him - I'm a surgeon, it may be nothing, but you've got a shuffle, just go to the GP and get it checked out."
He added: "It was a chance encounter and seemed to be the right thing to do. I think I did it tactfully."
Dr Fettke said he is glad to hear that Connolly followed his advice and went to see a doctor.
Last September the comedian revealed he had undergone cancer surgery and was being treated for Parkinson's disease.
He said the minor surgery in the US to deal with the very early stages of prostate cancer had been a success and that he was receiving the appropriate treatment for Parkinson's.
Dr Fettke said: "I just hope there's some free tickets in it somewhere."
Connolly is due to return to the stage next month, when he plays five gigs in America before undertaking a tour of New Zealand in April and May.