The two-time World Championship finalist was diagnosed with the illness last month but had successful surgery and has now received more good news from his oncologist.
"Just had the best news ever! I've got the all clear!" he wrote on Twitter.
"Will be back in action in the Shanghai Masters. Thank you everyone for all your support!"
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 occasions.