The 85-year-old Bannister became part of British sporting folklore when he ran three minutes 59.4 seconds at the Iffley Road Stadium near Oxford in 1954.
Bannister celebrated the 60 anniversary of that run only last February and is former a neurologist himself.
However, he admitted that he has been battling the illness for the past three years.
"I am having troubles with walking. Ironically, it's a neurological disorder - Parkinson's disease," he told the BBC.
"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, there's a gentle irony to it.
"I am being well looked after and I don't intend to let it interfere - as much as I can.
"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 won gold medals for Britain in the Commonwealth Games and the European Championships in 1954 having just missed out on a medal at the 1952 Olympics in Helsinki.
He was part of the London 2012 torch relay and carried the torch around the same track where he completed his most famous run.
"I know quite a lot about (Parkinson's) and have treated a lot of people with it," a reflective Sir Roger said.
"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."
- Sports & Recreation