  In this paper, we investigate Einstein hypersurfaces of the warped product
$I\times_{f}\mathbb{Q}^{n}(c)$, where $\mathbb{Q}^{n}(c)$ is a space form of
curvature $c$. We prove that $M$ has at most three distinct principal
curvatures and that it is locally a multiply warped product with at most two
fibers. We also show that exactly one or two principal curvatures on an open
set imply constant sectional curvature on that set. For exactly three distinct
principal curvatures this is no longer true, and we classify such hypersurfaces
provided it does not have constant sectional curvature and a certain principal
curvature vanishes identically.
