The Sweet Caroline singer, who turns 77 on Wednesday, said he had made the decision with “great reluctance and disappointment” and thanked fans for their support.
The onset of the disease is said to have made it “difficult” for Diamond to “travel and perform on a large-scale basis”.
However the singer reassured fans that he plans to continue to write and record music “for a long time to come”.
“It is with great reluctance and disappointment that I announce my retirement from concert touring,” he said in a statement on his website.
“I have been so honoured to bring my shows to the public for the past 50 years.
“My sincerest apologies to everyone who purchased tickets and were planning to come to the upcoming shows.
“I plan to remain active in writing, recording and other projects for a long time to come.
“My thanks goes out to my loyal and devoted audiences around the world. You will always have my appreciation for your support and encouragement. This ride has been ‘so good, so good, so good’ thanks to you.”
Diamond was due to embark on the third leg of his 50th anniversary tour in Australia and New Zealand in March.
The gigs followed concerts in Europe, including the UK and Ireland, and the US in 2017.