No. Prawns are crustaceans (invertebrates with a hard outer shell), not fish. Fish are vertebrates with a backbone and gills; prawns belong to the same broad group of shelled decapod crustaceans as shrimp, crabs, and lobsters.
Common names blur the line: in the United States, “shrimp” is often used for many shrimp-like crustaceans regardless of size, while in Britain and elsewhere “prawn” is a frequent everyday label for similar animals. NOAA notes that prawns and shrimp are closely related crustaceans whose names are used loosely in everyday speech, with only modest anatomical differences between true prawns and shrimp.
Source: How do prawns, crayfish, and shrimp differ? — NOAA Fisheries