The sustainability of Machine Learning-Enabled Systems (MLS), particularly with regard to energy efficiency, is an important challenge in their development and deployment. Self-adaptation techniques, recognized for their potential in energy savings within software systems, have yet to be extensively explored in Machine Learning-Enabled Systems (MLS), where runtime uncertainties can significantly impact model performance and energy consumption. This variability, alongside the fluctuating energy demands of ML models during operation, necessitates a dynamic approach. Addressing these challenges, we introduce EcoMLS approach, which leverages the Machine Learning Model Balancer concept to enhance the sustainability of MLS through runtime ML model switching. By adapting to monitored runtime conditions, EcoMLS optimally balances energy consumption with model confidence, demonstrating a significant advancement towards sustainable, energy-efficient machine learning solutions. Through an object detection exemplar, we illustrate the application of EcoMLS, showcasing its ability to reduce energy consumption while maintaining high model accuracy throughout its use. This research underscores the feasibility of enhancing MLS sustainability through intelligent runtime adaptations, contributing a valuable perspective to the ongoing discourse on energy-efficient machine learning.