The news from his family comes as the Mets are preparing to mark the 50th anniversary of their 1969 World Series victory.
Seaver is a living baseball legend, nicknamed "Tom Terrific" and "The Franchise," who was once considered the heart of the team.
The famed pitcher with the champion 1969 Miracle Mets is now taking on perhaps his toughest opponent in his 74 years.
Web Extra: CBS2's Otis Livingtson Talks Tom Seaver's Dementia Diagnosis
"When I heard it today, it was a little bit of a shock, but I also understood," said former teammate Art Shamsky.
Shamsky said when he met Seaver about a year and a half ago to work on the soon-to-be-released book, "After the Miracle," Shamsky knew then something was off.
"Hopefully he'll be able to deal with it, the family will be able to deal with it," he said. "I hate to use the word 'was,' because I feel like it still is, but - Tom was a very, very special person."
The Seaver family said in a statement, "The family is deeply appreciative of those who have supported Tom throughout his career, on and off the field, and who do so now by honoring his request for privacy."
They said he will continue to work on his beloved winery at his California home, but his health will prevent him from attending the 50th anniversary of the Miracle Mets celebration in June. So the team is planning to honor him with other tributes, which will include his family.
Fellow Hall of Famer Mike Piazza tweeted, "So sad to hear Tom Seaver has dementia. He will always be the heart and soul of the @Mets ,the standard which all Mets aspire to, this breaks my heart. Do not feel worthy to be mentioned in the same breath, yet honored to be with him in the @baseballhall #Mets #MLB"
For Mets fans, like Justin Cabrera who named his puppy Seaver after his baseball hero, the news was a shock.
"Very difficult for us to be hearing this news now about our longtime favorite," he said.
"It's very sad. He's such a great ball player," said fan Nestor Wachoski.
"It's hard to argue who would be better than him and what he meant to the team, and the franchise and the city," Shamsky added.
Until 2016, Seaver held the highest vote percentage for Hall of Fame induction at 98.84 percent. His 20-year career included three Cy Young Awards, 12 All Star game appearances and that 1969 World Series win.
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