The 49-year-old, who has been plagued by neck, back, shoulder and arm pain, won the 2002 world title, beating Stephen Hendry in an 18-17 final thriller.
He was also a two-time runner-up.
“I had an MRI scan about seven weeks ago which picked up significant wear and tear in my neck,” Ebdon said.
“Two of the vertebrae need to be replaced, which is not an operation I want to have because if it went wrong I could be in a wheelchair for the rest of my life.
“It’s far too risky. The professor explained to me that it wouldn’t be a cure. It could work, but it could make things worse and I would probably need to have it again in 10 years.”