Meat is defined as the flesh of an animal so, technically speaking, shrimp is meat. Shrimp has a hard exterior shell and lives in a sea, so it is classified as a crustacean or shellfish, which is often differentiated from the meat of land animals, usually for religious purposes.
The Jewish religion, for instance, forbids the consumption of shellfish. So, although the Jewish religion does not strictly forbid meat, it does differentiate between the types of meat that its followers may consume and the classification of shellfish. Similarly, during lent, Catholics may only consume fish on Fridays. For all intents and purposes, shrimp is classified as a fish by the Catholic religion and may be eaten on Fridays.