The 73-year-old was taken to hospital last week for urgent surgery, with part of his jaw reportedly removed at a Melbourne hospital.
His family confirmed the cancer had been in his mouth.
In a further update today, they thanked the public for their ongoing support.
“John remains in a stable condition in ICU (intensive care) following the removal of a cancerous tumour in his mouth on Tuesday,” wife Jill Farnham said.
“He is awake and responding well to the care he’s receiving.”
Music industry stalwart Molly Meldrum was among those wishing the You’re The Voice singer the best in his operation and recovery last week.
“He has been a friend of mine for a very long time, and we have been through lots in that time,” he told 9News.
“He is the voice, there is doubt about that and he will always be the voice.”
Prime Minister Anthony Albanese also praised the music icon as a great Australian.
Farnham has been a mainstay of Australian entertainment since he was billed as teen idol “Johnny Farnham” in the late 1960s.
The 73-year-old’s 1986 album Whispering Jack, featuring the single You’re The Voice, remains the second-highest selling album in Australia, behind only Meat Loaf’s Bat Out Of Hell (1977).
He has received 19 ARIA awards, and was named an Officer of the Order of Australia in 1996, and Australian of the Year in 1987.