We study the relation between the supersymmetry breaking patterns and the gauge couplings, prepotential of four-dimensional $\mathcal{N}=2$ gauged supergravity. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet which parametrizes SO$(4,1)/{\rm{SO}}(4)$ coset. We derive the expressions of two gravitino masses under the general gauging based on the embedding tensor formalism, and discuss their behaviors in some concrete models. Our approach would be important when we discuss the relation with the flux compactification, and the application to particle and cosmological phenomenology.