Energy consumption in Information and Communication Technology (ICT) is a large portion of total energy consumed in industrial countries. Virtualized Network Environment (VNE) has recently emerged as a solution to address the challenges of future Internet. It is essential to develop novel techniques to reduce VNE's energy consumption. In this paper, we propose an energy saving method that optimizes VNE's energy consumption during the off-peak time. This method reconfigures mapping for some of the embedded virtual links in the off-peak period. The proposed strategy enables providers to adjust the level of the reconfiguration, and accordingly control probable traffic disruptions due to the reconfiguration. This problem is formulated as a Binary Integer Linear Program (BILP). Since the defined BILP is NP-hard, a novel heuristic algorithm is also suggested. The proposed energy saving methods are evaluated over random VNE scenarios. The results confirm the defined solutions are able to save notable amounts of energy during off- peak period, while still accommodating off-peak traffic demands of involved virtual networks.