The popular 33-year-old, nicknamed 'The Captain' as he is a licensed pilot, learned the news last week and will have surgery on Tuesday.
Carter will then undergo chemotherapy after his surgery but he has vowed to return to the snooker tour.
Carter has battled back from illness in the past – in 2003 he was diagnosed with Crohn's disease but recovered to become one the best players on the snooker tour.
"I hope to be back in action soon," he said about his latest battle.
World Snooker chairman Barry Hearn added: "Ali has shown in his battle against Crohn's disease that he is a fighter. We hope for a positive outcome and everyone in snooker is 100 per cent behind him. We look forward to seeing him back on the circuit soon."
Carter has won three ranking events in his career and has been ranked as high as number two in the world.
He reached the World Championship final at the Crucible in both 2008 and 2012 losing to Ronnie O'Sullivan on both occasion.