A statement says she died on Tuesday following complications from a recent urinary tract infection.
The cat from Arizona had "helped millions of people smile".
Grumpy, whose real name was Tardar Sauce, went viral in 2012 after photographs of her sour expression emerged online. Her image quickly spread as a meme.
According to owner Tabitha Bundesen, her facial expression was caused by feline dwarfism and an underbite.
Grumpy Cat travelled the world making television appearances and in 2014 even starred in her own Christmas film.
Madame Tussauds in San Francisco unveiled a waxwork of her in 2015.
Her Instagram account has more than two million followers.
Grumpy's face has starred in thousands of memes with many people choosing to share them again after hearing the news of her death.