Heterogeneous cloud radio access networks (H-CRANs), proposed to boost both spectral and energy efficiency while reducing the signaling overhead, have been regarded as a promising paradigm for fifth-generation wireless communication systems. To reduce the network power consumption, in this paper, we propose a joint remote radio head (RRH) activation and outage constrained coordinated beamforming (CoBF) algorithm for massive multiple-input multiple-output H-CRANs. Considering the imperfect channel state information and power consumption of fronthaul links and individual transmission power limitations at the RRHs, the downlink network power minimization problem subject to the constraints of specified outage probabilities at each macro user equipment (MUE) and each RRH user equipment (RUE) is reformulated. For a given RRH activation set, we first derive a conservative convex approximation for the outage constraints of RUEs by using semidefinite relaxation and an extended Bernstein-type inequality, while a closed-form expression is obtained for the outage constraints of MUEs. Then, we reformulate the nonconvex problem into a semidefinite program. Moreover, we propose a low-complexity algorithm to perform the joint optimization of the RRH activation and robust CoBF by using the group sparse beamforming method through the weighted 11/12 norm reformulation, where the group sparsity patterns of beamformers are used to guide the RRHs that can be switched off. Simulation results demonstrate that the proposed algorithm can significantly reduce the network power consumption by 28% in the low signalto-interference-plus noise ratio scenario. In addition, the algorithm can approach the system performance of the exhaustive search algorithm while having a much lower computational complexity.