The Scotsman has suffered with gallstones for a number of months and had keyhole surgery to try and resolve the issue.
His medical procedure means the 52-year-old will miss the next three World Series of Darts tournaments which take place in Australia and New Zealand.
The two-time conqueror of the infamous Alexandra Palace said he had to put his health above his darting career.
Wright said on Twitter: "So surgery day is here, finally.
"I'm sorry to all my fans who expected 2 see me in Australia & New Zealand, but I had 2 make the choice between my health or the darts, unfortunately for my fans it was my health that won. I'm very nervous but I have @jowrighty8 by my side as always."
Wright's wife and manager Joanne later used his Twitter account to provide an update.
She wrote: "Peter's out of surgery, all went well. Just need to take time to recover and follow doctors orders now."
Wright admitted ahead of last month's World Matchplay tournament in Blackpool that the problem could flare up at any time.
He said: "It could flare up at any moment, I am just trying not to eat crumpets caked in butter."