In this paper, we study Einstein doubly warped product Poisson manifolds. First, we provide necessary and sufficient conditions for a doubly warped product manifold (M=Bf×bF,g,Π), equipped with a Poisson structure Π to be a contravariant Einstein manifold. Additionally, under certain conditions on the base space B, we prove that if M is an Einstein doubly warped product Poisson manifold with non-positive scalar curvature, then M is simply a singly warped product Poisson manifold. We also investigate the existence and non-existence of the warping function on the base space B associated with constant scalar curvature on M, assuming that the fiber space F has constant scalar curvature.