Not sure what you count as short (or if some of them are “classics”) but some of the ones I enjoyed include:
1984 (George Orwell)
Night (Elie Wiesel) - this one is a trilogy if you really enjoy it
Fahrenheit 451 (Ray Bradbury)
Hatchet (Gary Paulsen)
To Kill a Mocking Bird (Harper Lee)
100 years of solitude (Gabriel García Márquez)
Great expectations (Charles Dickens)
The Odyssey (Homer)