Bannister, 85, made the admission in a BBC Radio Oxford documentary to mark the anniversary of his famous run in the city, which will be broadcast on Friday.
Bannister, who went on to have a distinguished career as a neurologist following his retirement from athletics, said: "I am having troubles with walking. Ironically it is a neurological disorder - Parkinson's.
"There's a gentle irony to it. I have seen and looked after patients with so many neurological and other disorders that's I am not surprised I have acquired an illness. It's in the nature of things.
"I am being well looked after and I don't intend to let it interfere - as much as I can."
Bannister said he was diagnosed with the condition three years ago but has refrained from speaking publicly about it until now.
He added: "Just consider the alternatives - that is the way I look at it.
"One of my pleasures in life - apart from running - has been walking. Intellectually I am not (degenerating) and what is walking anyway!"
Bannister broke the fabled barrier on May 6, 1954 at Oxford's Iffley Road Track with the help of Sir Christopher Chataway and Chris Brasher who acted as pacesetters.
Brasher died in 2003 after a short illness and Chataway died of cancer in January this year.
Bannister's interest in neurology was one of the main reasons for his decision to curtail his athletics career after the 1964 European Championships.
In an interview with the Guardian in 2004, Bannister said: "I had always wanted to become a neurologist, which is one of the most demanding vocations in medicine.
"Where do you stop, after all, with the brain? How does it function? What are its limits? The work seems unending."
Bannister later went on to become a Master of Pembroke College, Oxford.
He told the programme he believes there is much work still to do before a cure for the condition with which he has been afflicted can be found.
Bannister added: "I know quite a lot about [Parkinson's] and have treated a lot of people with it.
"I am aware of all the research that's been done. I think it will take some time before there is a breakthrough. But the management and drug treatments are improving all the time."
Sir Roger Bannister may be best remembered for running the first sub-four minute mile, but the man himself is more proud of his Commonwealth gold medal.
Bannister said his exploits at the 1954 Commonwealth Games, only months after breaking the four-minute barrier, which saw him win mile gold were a greater achievement.
The race in Vancouver was between Bannister and Australia's John Landy, who had broken the Briton's record just 46 days after it had been set, and was dubbed the 'Miracle Mile'.
Bannister took the title in a Games record 3mins 58.8secs, leaving Landy, who clocked 3:59.6, to take the silver.
"I think that racing in the Olympics and Commonwealths is more important than breaking records," Bannister said.
"Vancouver was the pinnacle of my athletics career. It is very difficult to break records during Olympic competition, but winning races was better than holding world records.
"I had achieved the record, but by this time there was no doubt that I had to beat John Landy, who had by then become the world-record holder.
Bannister said going head-to-head with the new record holder, who had been the favourite for Commonwealth gold, was the true yard-stick by which the duo could be compared.
Landy led for most of the race, but Bannister overtook him on the final bend as the Australian looked round to check where he was and then held on to take the title.
"The race between the two of us was a very, very special race," he said.
"It determined which would be regarded as the superior runner in history, not the not the sub four minutes, but the head-to-head nature of the race in Vancouver.
"He was the favourite by then and he was probably a stronger runner, but I had a stronger finish.
"I just had to hang on as much as I could when he was trying to run me off my feet, but I managed to hang on and overtake him.
"I had to overtake him on the bend and I knew the only place he could look and see if he had dropped me was on the last corner, so I left it so we were just at the edge and, fortuitously, he looked over his shoulder and I overtook him."
A bronze sculpture of the moment Landy glanced round and lost the race stands outside the Pacific National Exhibition in Vancouver, having been re-homed following the demolition of the Empire Stadium.
It is a lasting legacy of a rivalry, and a victory which marked the highlight of Bannister's athletics career.