The beloved media personality was aged 60.
“Thank you Fabrizio for all the love you gave us,” his wife Carlotta, his brother Fabio and the rest of his family said in a statement.
Mr Frizzi - who presented prime-time shows on Italian State broadcaster RAI - had to take time out after suffering from ischaemia in October last year, but had recently returned to his show ‘L'Eredità’ (The Inheritance).
Upon his return to the show in December, Mr Frizzi said: “[Presenting] ‘L'Eredità’ is a joy; it’s good for my health.”
“I feel that the adrenalin helps me get better,” he added.
RAI paid tribute to Mr Frizzi in a statement on Monday.
“From children’s television to prime-time, over a 40-year career, he was a fresh-faced figure, totally beloved by the public,” the statement read.
“He was a great artist and show business figure.
A man of smiles, with hugs for all.”
RAI said Mr Frizzi’s body will lie in state at the broadcaster’s headquarters on Rome’s Viale Mazzini on Tuesday.
His funeral will take place at noon on Wednesday at the Chiesa degli Artisti in Piazza del Popolo.
As tributes poured in from politicians and fellow entertainers, veteran RAI presenter Pippo Baudo said: “He was a man who loved his work.”
La7 news chief Enrico Mentana also paid his respects to Mr Frizzi, saying “it was impossible not to love him”.
With ANSA