Knotts died Friday night of pulmonary and respiratory complications at a Los Angeles hospital, said Paul Ward, a spokesman for the cable network TV Land, which airs his two signature shows.
Griffith, who remained close friends with Knotts, said he had a brilliant comedic mind and wrote some of the show's best scenes.
"Don was a small man...but everything else about him was large: his mind, his expressions," Griffith told The Associated Press on Saturday. "Don was special. There's nobody like him."
"I loved him very much," Griffith added. "We had a long and wonderful life together."
Born Jesse Donald Knotts in West Virginia, Knotts started show business as a ventriloquist and became a comedian while in the Army. His first big break was "No Time For Sergeants," which starred his future partner, Andy Griffith.
Unspecified health problems had forced Knotts to cancel an appearance in his native Morgantown in August.
Knots's half-century career included seven TV series and more than 25 films, but it was the Griffith show that brought him TV immortality and five Emmys.
The show ran from 1960-68, and was in the top 10 of the Nielsen ratings each season, including a No. 1 ranking its final year. It is one of only three series in TV history to bow out at the top: The others are "I Love Lucy" and "Seinfeld." The 249 episodes have appeared frequently in reruns and have spawned a large, active network of fan clubs.
As Griffith's bug-eyed and accident-prone deputy, Knotts carried a bullet in his shirt pocket, not his gun. His constant fumbling, a recurring sight gag, was typical of his self-deprecating humor.
Knotts, whose shy, soft-spoken manner was unlike his high-strung characters, once said he was most proud of the Fife character and doesn't mind being remembered that way.
His favorite episodes, he said, were "The Pickle Story," where Aunt Bea makes pickles no one can eat, and "Barney and the Choir," where no one can stop him from singing.
"I can't sing. It makes me sad that I can't sing or dance well enough to be in a musical, but I'm just not talented in that way," he lamented. "It's one of my weaknesses."
Knotts appeared on several other television shows. In 1979, he replaced Norman Fell on "Three's Company," also starring John Ritter, Suzanne Somers and Joyce DeWitt.
Early in his TV career, he was one of the original cast members of "The Steve Allen Show," the comedy-variety show that ran from 1956-61. He was one of a group of memorable comics backing Allen that included Louis Nye, Tom Poston and Bill "Jose Jimenez" Dana.
Knotts' G-rated films were family fun, not box-office blockbusters. In most, he ends up the hero and gets the girl - a girl who can see through his nervousness to the heart of gold.
In the part-animated 1964 film "The Incredible Mr. Limpet," Knotts played a meek clerk who turns into a fish after he is rejected by the Navy.
When it was announced in 1998 that Jim Carrey would star in a "Limpet" remake, Knotts responded: "I'm just flattered that someone of Carrey's caliber is remaking something I did. Now, if someone else did Barney Fife, that would be different."