Large-scale distributed antenna systems with many access points (APs) that serve the users by coherent joint transmission is being considered for 5G-and-beyond networks. The technology is called Cell-free Massive MIMO and can provide a more uniform service level to the users than a conventional cellular topology. For a given user set, only a subset of the APs is likely needed to satisfy the users performance demands, particularly outside the peak traffic hours. To find achieve an energy-efficient load balancing, we minimize the total downlink power consumption at the APs, considering both the transmit powers and hardware dissipation. APs can be temporarily turned off to reduce the latter part. The formulated optimization problem is non-convex but, nevertheless, a globally optimal solution is obtained by solving a mixed-integer second-order cone program. Since the computational complexity is prohibitive for real-time implementation, we also propose two low-complexity algorithms that exploit the inherent group-sparsity and the optimized transmit powers in the problem formulation. Numerical results manifest that our optimization algorithms can greatly reduce the power consumption compared to keeping all APs turned on and only minimizing the transmit powers. Moreover, the low-complexity algorithms can effectively handle the power allocation and AP activation for large-scale networks.