Soft-defined networking (SDN) is a new approach that enables operators to easily manage all the network elements. In this paper, we address the problem of energy-aware routing in SDN-based carrier-grade Ethernet networks. Our approach is based on turning off network nodes and links to reduce energy consumption, while respecting the rule space capacity for each Openflow switch, and maintaining an allowable maximum link utilization. The problem of identifying the optimal set of network elements to be turned off is NP-hard. We first present an exact model based on an integer linear programming formulation for the problem. Then, we describe a set of first-fit heuristic algorithms suitable for large-sized networks. The exact and heuristic approaches are tested on SNDlib-based instances. Experimentations show the efficiency of both exact and heuristic methods for different network topologies. In particular, our heuristic algorithms are able to achieve a good balance between energy consumption, resource utilization, and network performance.