We study hypersurfaces in pseudo-Riemannian real space forms of non-zero sectional curvature, which write as a warped product of a 1-dimensional base with an (n − 1)-manifold of constant sectional curvature. We show that either they have constant sectional curvature or they are contained in a rotational hypersurface. Therefore, we first define rotational hypersurfaces in indefinite real space forms of non-zero sectional curvature.