Cloud radio access network (C-RAN) and massive multiple-input-multiple-output (MIMO) are two key enabling technologies for 5G as they improve radio performance while lowering the cost of operation. In a C-RAN system with massive MIMO-based remote radio units (RRUs), fronthaul is often the bottleneck in practice due to its finite capacity. To reduce the capacity requirements on fronthaul, precoding is done at the RRUs. In this paper, we maximize the energy efficiency (EE) of such a system by optimizing the transmit powers while explicitly incorporating the capacity constraints on fronthaul. We develop a successive convex approximation (SCA) algorithm, which is guaranteed to converge to a local optimum. Towards this, we propose novel bounds on the user rate function, which facilitates a convex approximation of the EE maximization problem. The convex problem is solved in each SCA iteration through Dinkel-bach's algorithm and dual decomposition. Numerical results show that the proposed algorithm significantly improves EE compared to the case with no power control and outperforms the weighted minimum mean square error algorithm. © 2019 IEEE.