Due to emerging requirements and pressures related to environmental protection, manufacturing enterprises have expressed growing concern for adopting various energy-saving strategies. However, environmental criteria were usually not considered in traditional production scheduling problems. To overcome this deficiency, energy-saving scheduling has drawn more and more attention from academic scholars and industrial practitioners. In this paper, an energy-saving flexible job shop scheduling problem (EFJSP) is introduced in accordance with the criterion of optimizing power consumption and processing costs simultaneously. Since the classical FJSP is strongly NP-hard, an Improved Sparrow Search Algorithm (ISSA) is developed for efficiently solving the EFJSP. In the ISSA, a Hybrid Search (HS) method is used to produce an initial high-quality population; a Quantum Rotation Gate (QRG) and a Sine–Cosine Algorithm (SCA) are integrated to intensify the ability of the ISSA to coordinate exploration and exploitation; the adaptive adjustment strategy and Variable Neighborhood Search (VNS) are applied to strengthen diversification of the ISSA to move away from local optima. Extensive computational experiments validate that the ISSA outperforms other existing algorithms in solving the EFJSP due to the advantages of intensification and diversification mechanisms in the ISSA.