Carter, 34, will face an intensive course of chemotherapy, World Snooker said in a statement.
The twice World Championship runner-up, a winner of three ranking titles, was due to play in the Wuxi Classic qualifiers in Gloucester on Saturday but has withdrawn from the event.
WPBSA Chairman Jason Ferguson said: “Ali is the toughest competitor I know and having spoken to him over the last few days I can assure everyone he has the fight to get through the battle ahead. I know that the world will be looking forward to Ali returning to action and I am sure that all of our friends, fans and partners will join with me in wishing Ali a full recovery."
Carter, from Colchester, was ranked as high as world number two before his first illness, and twice lost to Ronnie O’Sullivan in the 2008 and 2012 World Championship finals.
A sufferer of Crohn's disease, Carter was diagnosed with testicular cancer last summer, underwent surgery and returned to action one month later.
- Disease & Medical Conditions