The 76-year-old released a statement on Friday, revealing how he “could no longer ignore the symptoms”.
Parkinson’s is an incurable neurological disease that can cause tremors and affect coordination. Thinking and behavioural problems can also occur.
He wrote: “In the latter years of my life, I find it increasingly difficult to perform routine tasks, and getting around is more of a challenge.
“My family and I began to notice changes about three years ago. For a while, I resisted interrupting my work to visit a doctor. But as my daily physical struggles intensified, I could no longer ignore the systems, so I acquiesced.
“Recognition of the effects of this disease on me has been painful, and I have been slow to grasp the gravity of it.”
He noted that the same disease “bested my father”, Noah Lewis Robinson Sr, who died in 1997, aged 88.
Mr Jackson fought for civil rights alongside Martin Luther King in the 1960s and was twice nominated the Democratic presidential nominee in the 1980s.
He said he will continue work on his memoir, saying: “I steadfastly affirm that I would rather wear out than rust out.”