In this paper, we study the performance of cooperative millimeter wave (mmWave) networks with hybrid precoding architectures. Considering joint transmissions and BS silence strategy, we propose hybrid precoding algorithms which minimize the sum power consumption of the base stations (BSs), for both fully- and partially-connected hybrid precoding (FHP and PHP, respectively) schemes, for single-carrier and orthogonal frequency-division multiplexing systems. We reformulate the analog precoding part as an equal-gain transmission problem, which only depends on the channel information, and the digital precoding part as a relaxed convex semidefinite program subject to per-user quality-of-service constraints that gives the optimal sum power consumption in terms of the BS silence strategy. In order to reduce the complexity of the hybrid precoding algorithm with optimal BS silence strategy, we propose a sub-optimal hybrid precoding algorithm that iteratively put BSs with small power into the silent mode. The simulation results show that, depending on the parameter settings, the power consumption of the PHP may be dominated by the RF transmit power and it may result in a larger power consumption than the FHP. For the cases with 2 BSs and 4 users, implementation of the FHP and the PHP in cooperative networks reduces the required RF transmit power, compared to the case in a non-cooperative network, by 71% and 56%, respectively.