The 85-year-old Fitzgerald was taken to the Dublin city centre hospital earlier this week after falling ill and is currently on a ventilator.
He is surrounded by his family as doctors treat the man who was twice Irish Prime Minister in the 1980s.
“I’m aware that he is in hospital and on a ventilator and I know that his family has been called to his side,” said Kenny in New York.
“I say a prayer for his health and well-being. I hope that he makes it through. He’s an Irish institution that we don’t deserve to lose at this stage.”
Dr Fitzgerald maintained a high public profile after his final term in office as leader of the Fine Gael-Labor coalition in 1987.
John Bruton, another former Prime Minister, also wished him well.
“I think everybody who knows him is praying that he will make a recovery. He’s a tremendous asset to the country,” said Bruton.
A spokeswoman for Dr FitzGerald confirmed that he was being treated in hospital and said that medical staff were carrying out tests to diagnose the cause of the illness.