The Dublin-born comedian was due to take part in a tour of Ireland throughout July and August this summer.
However, a spokesperson for the 68-year-old has stated that the tour will no longer go ahead due to his faltering health.
"Brendan Grace has been in hospital for the last four weeks receiving treatment for pneumonia," Tom Kelly, business manager for Grace, told The Independent.
"It has now transpired that he is also suffering from cancer for which he is receiving ongoing care and treatment."
Kelly stated that Grace's family have been a "great support to him at this difficult time", and ask that their privacy be respected.
The manager added that the comedian is receiving treatment in Ireland, and will be remaining in hospital for the time being.
Approximately 47,000 new cases of lung cancer are diagnosed in the UK on an annual basis, Cancer Research UK states.
It is the third most common cancer in the UK, the charity says, and accounts for more than a fifth of cancer deaths across the country.
Grace's cancer diagnosis comes almost a year after he revealed he had suffered a stroke.
While speaking on documentary Brendan Grace: Funny Man, which aired on RTE in October 2018, the comedian said that he incorporated his experience of the stroke into his stage act.
“I had a stroke and I also had an accident that screwed up my gait. I now had to deliver the comedy from a seated position, only occasionally getting up from the chair," Grace said.
“My fear was always that people would think ‘this guy had had a few bevvies’, so what I did was, I made a virtue of my leg problem and built it into the act.”
Earlier this year it was announced that Father Ted actor Pat Laffan had passed away at the age of 79.
“All here will remember him first and foremost as our friend and mentor and we will miss him terribly,” Laffan's agency said in a statement.
“We send our heartfelt condolences to his friends and family.”