The 20-year-old, who was on loan at Scottish Premiership side Livingston, has played four times for the Norwich senior team.
Barden played youth football for Arsenal before joining Norwich and has also had a loan spell at Bury Town.
Barden, a Wales u-21 international, told Norwich’s official website: “It has been a very difficult and challenging period, but the support of my family, friends and colleagues has helped get me through the last few weeks.
“I can’t thank the medical departments at both Norwich and Livingston enough, as well as everyone at the Royal Marsden Hospital. The speed at which everything has moved has been crazy, but everyone has been absolutely brilliant with me. Both Daniel Farke and the Livingston manager, David Martindale, have also been very supportive.
“The initial diagnosis was a real shock for me, but the positive thing is that we’ve caught it early and the prognosis and next steps have all been positive.
“I’m optimistic and have a positive mindset. I’m confident that I’ll be able to beat it and that I’ll be back out there doing what I love soon.
“I’d like to thank everyone around me for their support. I know that the coming period will be challenging and would ask for privacy for me and my family at this stage. Where possible, I’ll do what I can to update on my progress.
“Thank you once again for the support. See everyone soon.”
Another Welsh footballer, Bournemouth’s David Brooks, announced last week that he had been diagnosed with stage two Hodgkin Lymphoma.