Mr McEntee (56), the Minister of State at the Department of Agriculture, left his family home yesterday morning to walk his dog, but was found dead a short time later.
The tragic passing has also stunned the world of sport: Mr McEntee was heavily involved in Meath GAA. His brother, Gerry, is a winner of two senior All-Ireland football medals.
Describing him as "a loyal friend and colleague", Mr Kenny said: "I am devastated at his sudden passing."
Friends say that Mr McEntee was stressed in the wake of the Budget, but was pleased to see a new redress scheme set up for households hit by the pyrite scandal.
He had long campaigned for the 10,000 homeowners affected.
Mr Entee was also credited with playing a major role in saving Mr Kenny's political career during the 2010 heave by members of his frontbench.
He is survived by his wife, Kathleen, mother Madge and children Vincent, Helen, Sally and Aoife.
President Michael D Higgins said that Mr McEntee had "made an enormous contribution to community and public life throughout his career in farming and agriculture, as a TD representing the people of Meath in Dail Eireann, and to the world of sport through his involvement with the GAA".
A clearly emotional Health Minister James Reilly said that his colleague was a "larger than life" individual who gave 100pc commitment to everything.
Mr McEntee first entered the Dail after a 2005 by-election to replace former Taoiseach John Bruton.
Mr Burton said the minister "was a man of unlimited emotional, and practical, commitment to any task he took on. It absorbed him totally. No effort was ever spared.
"He was a great success in politics. He leaves a gaping void in the life of his family, his county and his country," he said.
Former Meath football manager Sean Boylan summed up the sadness of all GAA members in the county, saying he could not believe Shane McEntee had died. He said he was "absolutely shocked" at his death.
"You just loved to see him come in. You loved his company," said Mr Boylan.
Tributes also came from outside Fine Gael and the GAA, with Labour's Pat Rabbitte fondly describing him as "a horse of a man".
"He would have been really fit. His brother was well known in GAA circles. It is terribly shocking."
Fianna Fail leader Micheal Martin said: "He was a true gentleman who commanded the genuine affection and respect of people on all sides of the House."
Sinn Fein President Gerry Adams added: "It was with shock that I learned the sad news today of the passing of Shane McEntee."
There was widespread shock within his native Meath, too, where preparations are under way for a funeral on Christmas Eve.
His Fine Gael colleague in Meath West, Ray Butler, said: "Life won't be the same without Shane. He was my best friend in the Dail."
His constituency colleague, Labour Meath East TD Dominic Hannigan, said the late minister was "always a very honourable man".
"He was extremely well liked in Meath and worked very hard for his constituents. I know he will be missed by all the people he has helped in his time in politics," he said.
Meath FF Senator Thomas Byrne said he was "always very kind and generous with his time. He will be sorely missed."