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."
"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.
"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."
"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.
#BREAKINGNEWS - Comedian Fred Willard died in his sleep last night at 86.— George Pennacchio (@abc7george) May 16, 2020
The sketch comedy master spent 50+ years in show biz.
Among his many movie credits: “Best In Show,” “Anchorman” & “WALL-E.”
On TV, “Fernwood Tonight,” “Modern Family” & “Jimmy Kimmel Live.”
May he R.I.P. pic.twitter.com/kInSrM8llY