Willard, a sketch-comedy master whose career in show business spanned more than 50 years, also appeared in such TV series as "Fernwood 2 Night" and "Modern Family."
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"He kept moving, working and making us happy until the very end," his daughter Hope Mulbarger said. "We loved him so very much. We will miss him forever."
News of Willard's death prompted an outpouring of condolences from fans and fellow actors on social media.
Fred Willard talks 'CATstravaganza' event that helps cats find homes
"How lucky that we all got to enjoy Fred Willard's gifts," Jamie Lee Curtis said on Twitter. "He is with his missed Mary now. Thanks for the deep belly laughs Mr. Willard."
Former co-star Michael McKean said he was "at a loss for words, a state Fred Willard never found himself in."
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"My friend for 40+ years, a great comic actor who had no competition because there was only one of him," McKean tweeted. "We were all so lucky. Goodbye, Fred."
Willard was also part of the cast of the new comedy series "Space Force," starring Steve Carell, which is set to premiere on Netflix on May 29.