The diagnosis forced Diamond to cancel a previously announced tour in Australia and New Zealand in March.
His wife, Katie, said Diamond's fans from Down Under have responded to the sad news in a positive and charitable way.
"Wow, I've received a bunch of messages from people in Aus & NZ who are donating their ticket refunds to good causes: Parkinson's research, animal rescue groups, fire victim funds, etc.," she tweeted, referring to Australia and New Zealand. "My heart is so full of joy to see this silver lining. Faith in humanity = restored. Thank you!"
Neil Diamond retweeted his wife's post.
"This makes me smile," he tweeted. "Thank you. Thank you to everyone for your outpouring of love and support. It makes a difference."
In his announcement Monday, Diamond wrote: "It is with great reluctance and disappointment that I announce my retirement from concert touring. I have been so honored 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."
He added, "I plan to remain active in writing, recording and other projects for a long time to come. My thanks go out to my loyal and devoted audiences around the world."
Diamond will turn 77 Wednesday, and on Sunday, he'll be honored with the Lifetime Achievement Award at the 60th Annual Grammy ceremony.