Space weather phenomena like geomagnetic disturbances (GMDs) and geomagnetically induced currents (GICs) pose significant risks to critical technological infrastructure. While traditional predictive models, grounded in simulation, hold theoretical robustness, they grapple with challenges, notably the assimilation of imprecise data and extensive computational complexities. In recent years, Tiny Machine Learning (TinyML) has been adopted to develop Machine Learning (ML)-enabled magnetometer systems for predicting real-time terrestrial magnetic perturbations as a proxy measure for GIC. While TinyML offers efficient, real-time data processing, its intrinsic limitations prevent the utilization of robust methods with high computational needs. This paper developed a physics-guided TinyML framework to address the above challenges. This framework integrates physics-based regularization at the stages of model training and compression, thereby augmenting the reliability of predictions. The developed pruning scheme within the framework harnesses the inherent physical characteristics of the domain, striking a balance between model size and robustness. The study presents empirical results, drawing a comprehensive comparison between the accuracy and reliability of the developed framework and its traditional counterpart. Such a comparative analysis underscores the prospective applicability of the developed framework in conceptualizing robust, ML-enabled magnetometer systems for real-time space weather forecasting.