DeFranco's family said the musician died on Wednesday evening at a Florida hospital.
His wife, Joyce, said his health had been poor in recent years.
DeFranco, a member of the American Jazz Hall of Fame, performed at venues around the world for 75 years and also recorded many albums.
The musician conducted the Glenn Miller Orchestra for eight years from 1966 to 1974.
He was named a National Endowment for the Arts Jazz Master and and later a Living Jazz Legend in a Kennedy Center ceremony.
And DeFranco won the Playboy All-Star award for top jazz clarinettist in the world 16 times.
"We have received condolences from around the world," DeFranco's wife told AP.
She said her husband's influence on music will last long beyond his lifetime.
Leading jazz clarinettist Ken Peplowski said: "Buddy DeFranco almost single-handedly was the clarinettist who moved the harmonic and rhythmic language forward from where Benny Goodman left off into the much more adventurous territory of bebop and beyond, while never forgetting his roots in swing music.
"He was also unfailingly kind and supportive to every other clarinettist who came after him."
Other top music stars he played with included Art Tatum, Ella Fitzgerald and Tony Bennett.
Originally named  Boniface Ferdinand Leonardo De Franco, the musician was born in Camden, New Jersey, but raised in south Philadelphia. He learned to play the mandolin at five, and took up the clarinet four years later.
He began his career as a teenager in Philadelphia and he went on to play with some of the major bands of his era including ones led by Tommy Dorsey, Count Basie, Gene Krupa and Charlie Barnett.
Later, composer Nelson Riddle was so impressed by DeFranco he wrote the musical Cross Country Suite in 1958 for him.
Legendary singer Nat King Cole, also introduced DeFranco when he premiered the work at the Hollywood Bowl.
Now, the annual Buddy DeFranco Jazz Festival is held each spring at the University of Montana.
DeFranco's family have asked that contributions in his memory be given to the festival so it can continue.
As well as his wife Joyce, the clarinettist is survived by his son Chad DeFranco.
Renowned jazz clarinettist Buddy DeFranco, known for working with Frank Sinatra and Billie Holiday and other well-known musicians, has died aged 91.