Gearóid Ó Cairealláin, whose son Naoise is a member of the hip hop group, passed away after a short illness.
He died on Friday, a day before the band perform at a sell-out gig at Belfast’s SSE Arena.
Mr Ó Cairealláin (67) headed Conradh na Gaelic between 1995 and 1998 and was a central figure in the 1991 establishment of Coláiste Feirste.
He suffered a stroke some years ago that left him paralysed from the waist down and in a wheelchair but continued to work on different projects promoting the Irish language.
Kneecap posted a tribute this afternoon which said: “Gearóid Ó Cairealláin, father of Móglái Bap, passed away last night.
“He was an Irish language revolutionary, community activist, loving father, husband and an inspiration to many.
“We are heartbroken.
“Tonight’s concert at the SSE Arena will be the largest Irish language gig in the city’s history. Nothing would have made him prouder. Tonight is for him.”
Paula Melvin, the current president of Conradh na Gaeilge, said Mr Ó Cairealláin was “a loved and cherished figure”.
“There can be no denying the incredible influence and impact Gearóid had on the Irish language movement, not only in Belfast, but throughout the country,” he said.
“He leaves behind him an undeniable legacy that will be an immense source of inspiration for us all throughout the future.”
Conchúr Ó Muadaigh, Conradh na Gaeilge advocacy manager, said society had lost “a giant, a leader, a great pioneer and activist of the Irish language movement”.
“He was, in many ways, the great architect of the modern revival, and the Irish language community as we know it today would simply not be here were it not for Gearóid and his colleagues,” he said.
He added: “Gearóid was resolute in his drive for language rights and equality, and tirelessly challenged the state and authorities for Irish language services.”
Mr Ó Cairealláin spent much of his professional life as a journalist.
In 1982 he set up the weekly paper, Preas an Phobail. He was a founder editor of the newspaper Lá, the only daily in any Celtic language.
After that he directed his attention to television journalism, and made a number of documentaries for BBC and TG4. These included Siobhán (a biography of the actress Siobhán McKenna), Sos Cogaidh/Ceasefire and Olc an Ghaoth, about New Orleans after Hurricane Katrina.
For the stage Mr Ó Cairealláin wrote 14 works in Irish.
In 2014 he wrote and performed his own one-man show, The Wheelchair Monologues, about his experiences of life after a catastrophic stroke.