The 49-year-old told Today FM that he had just completed two weeks of radiation and chemotherapy treatment.
"I have just started a journey with cancer," he told presenter Matt Cooper.
He said the diagnosis was a "huge shock" but that he had "caught it really early" and was "incredibly lucky".
The singer, who has had chart success with singles A Better Man and Life Love and Happiness, said he got a clean bill of health from his GP earlier this year but felt that "something was out of kilter".
He was diagnosed with a rectal tumour after undergoing a colonoscopy.
Kennedy said that he advised anyone with a "grain of doubt" over their health to get it checked.
He said he had also met with his brother, and fellow musician, Bap Kennedy after being "estranged for a very long time".
Bap Kennedy is receiving palliative care after being diagnosed with pancreatic cancer.
"Estrangement becomes like a very bad habit," Brian said, "It just becomes the norm. We just got used to not hearing or seeing from each other.
"I got to see him again and give him a hug and if anything good has come out of this, it was the chance to see him again.
"I think that cancer puts manners on the best of people, the best of situations and the worst."
Belfast singer-songwriter Brian Kennedy has revealed that he is being treated for rectal cancer.