There are really two answers to this question. Modernism can be used to describe a specific period in literature, art, and culture, and modernism can be used to describe an aesthetic style and approach. Orwell's Animal Farm, which was subtitled a Fairy Story, came out in 1945, so it can be seen as part of the modernist ear, although one could argue that the high modernist period was the 1920s, which produced seminal works like Ulysses, The Wasteland, Mrs. Dalloway, and Pound's first Cantos. Within this context, Animal Farm has little in common with these works. Orwell was a contemporary of these writers, but I don't think he can be considered a modernist, especially compared to them.
M.H. Abrams defines the characteristics of modernism as "new and distinctive features in subjects, forms, concepts, and styles of literature and the other arts in the early decades of the present, century, but especially after World War I (1914-1918)." Orwell may have shared in the post-war disillusionment and cynicism about human nature, but he was not particularly interested in experimental language or exploring new forms. In fact, in his celebrated "Politics and the English Language," he called for clarity and directness in writing, and Animal Farm is using a very old form, that of the animal fable.
A final difference between Animal Farm and many modernist works is the political nature of the book. While many modernist writers had political leanings (Pound was a notorious fascist), few of their works dealt as directly with politics as Orwell did in Animal Farm—which is about Stalinism—and his other books.
M.H. Abrams, A Glossary of Literary Terms, Sixth Edition.