The growth of Cloud computing has enabled scalable and accessible services, while also intensifying concerns over energy consumption, carbon emissions, and both the environmental and financial sustainability of data centers. Microservice architectures offer promising opportunities for granular resource optimization and energy savings, though it can also introduce complexities. It is crucial to investigate how microservice-based Cloud applications address energy efficiency. For this purpose, we conducted a systematic literature review (SLR) aiming to establish an overview of the state-of-the-art on energy-efficient microservice-based Cloud applications. The research questions of the SLR focus on revealing: (i) strategies to mitigate energy inefficiencies in microservice-based Cloud applications; (ii) experimental methodologies used to assess the effectiveness of the proposed strategy, and (iii) mechanisms for measuring energy consumption. As a result, 25 studies were selected and synthesized to provide a comprehensive overview about the topic. This paper also presents a taxonomy and raises important challenges and potential directions for future research.