They also confirmed Brendan had cancelled his July and August tour.
The spokesperson said Brendan would be remaining in hospital for ongoing treatment.
Following the news of his death, stars took to Twitter to pay tribute to the comedian.
Mrs Brown’s Boys favourite Brendan O’Carroll wrote: “So sad at the passing of a great comedy legend, husband and father #BrendanGrace.
“He opened doors for so many of us and leaves a legacy of love and laughter that will echo through this land and we will all mourn his passing.
“Rest peacefully Bottler you’ve earned it,” he added.
Brendan was known for playing Father Stack in Father Ted, playing the rude character in the comedy’s second series back in 1996.
He also appeared in Backyard Ashes and Moondance.
In a 2018 documentary about his life, Brendan Grace: Funny Man, he spoke about suffering with his health in recent years, revealing he had had a stroke and lost some of his toes due to gangrene caused by diabetes.
Brendan had been living in the US with his wife Eileen and their four children.
“My very best friend is Eileen,” he said in the programme. “There’s nothing I wouldn’t do for her and there’s nothing she wouldn’t do for me, and that’s how it’s been for the past 45 years. Doing nothing for each other.”
He also opened up about his health issues, saying: “I got diabetes. It was a bit of a blow to me.
“Eileen often said to me about the diabetes that she wished it was her who got it because she would be better ale to discipline herself into the right thing to do, whereas I’m inclined to throw caution to the wind.”
He also said he was now having to perform his comedy from sitting down after the stroke “screwed up [his] gait”.
“My fear was that people would think, ‘This guy has had a few bevvies,’ so what I did was, I made a virtue of my leg problem and built it into the act,” he added.