Bully Boy, who won the PDC World Championship after beating Michael van Gerwen in 2023 - the match that included the now infamous "greatest leg ever" - revealed the diagnosis via a statement after he was knocked out of the World Masters in Milton Keynes on Thursday by Danny Noppert.
"I broke both my wrists when I was 19 and now it's catching up with me, and I'm now suffering with arthritis to my right hand," Smith said.
"This isn't sympathy or a cry for help. This is letting you all into it.
"I've never given up or stopped from any pain.
"I see the specialist Monday and when I know, you will know, what will happen over the next month or so," the 34-year-old added.
"I'll never let anything beat me and I promise I'll be back very, very quickly."
He went into the latest World Championship ranked third in the world but was eliminated in his first match by Kevin Doets in his opening fixture.
That result sent Smith's world ranking tumbling down to 16th and meant he missed out on a place in the upcoming Premier League Darts competition.
Arthritis is a common condition that causes pain and inflammation in a joint.
It is different from common cases of dartitis, which is a mental condition that prevents dart players from releasing the dart at the right time. It's similar to "the yips", which is a term used to describe a loss of fine motor skills in other sports.