In this paper, we develop an energy-based static and dynamic control framework for stochastic port controlled Hamiltonian systems. In particular, we obtain constructive sufficient conditions for stochastic feedback stabilization that provide a shaped energy function for the closed-loop system while preserving a Hamiltonian structure at the closed-loop level. In the dynamic control case, energy shaping is achieved by combining the physical energy of the plant and the emulated energy of the controller. Several numerical examples are presented that demonstrate the efficacy of the proposed passivity-based stochastic control framework. (C) 2018 Elsevier Ltd. All rights reserved.