We consider the problem of channel estimation for millimeter wave communications (mmWave). We formulate channel estimation as a structured sparse signal recovery problem, in which the signal structure is governed by a priori knowledge of the channel characteristics. We develop a Bayesian group sparse recovery algorithm which takes into account for several features unique to mmWave channels, such as spatial (angular) spreads of received signals and power profile of rays impinging on the receiver array. We validate the developed method via numerical simulations and demonstrate an improved estimation performance relative to the existing methods.