To achieve accurate and reliable predictions of groundwater drought, it is essential to incorporate relevant meteorological variables and apply advanced predictive methodologies capable of modeling their complex interrelationships. In this study, groundwater drought prediction models were developed based on the seven modified drought indices, which are obtained from groundwater levels and multiple meteorological parameters. The analysis focuses on four districts in Türkiye (Tekirdağ-Çorlu, Tekirdağ-Çerkezköy, Amasya-Merzifon, and Amasya-Centre), which are hereafter referred to collectively as the study areas. Three machine learning models were applied such as a standalone Artificial Neural Network (ANN) and two hybrid models, ANN integrated with Shuffled Frog Leaping Algorithm (SFLA-ANN) and Firefly Algorithm (FFA-ANN). The hybrid metaheuristic algorithms were chosen for their ability to model nonlinear and complex relationships between meteorological variables and groundwater levels, which traditional statistical methods cannot fully capture. Modified drought indices were employed to represent the groundwater drought better. The findings indicate that the hybrid FFA-ANN model generally provides the highest predictive accuracy for most indices, with coefficient of determination values frequently exceeding 0.90. In contrast, the ANN model occasionally outperforms the hybrid FFA-ANN model in terms of root mean square error (RMSE) for specific stations within the study areas. These results highlight the robustness of hybrid ANN approaches, especially FFA-ANN, in predicting groundwater drought under changing climate conditions. The novelty of this study is the modification of meteorological drought indices widely used to represent groundwater drought and the application of hybrid metaheuristic ANN models to estimate these indices in Türkiye. The results demonstrated that such models provide a reliable framework for predicting groundwater drought and provide decision-makers with advanced tools for water resources management, irrigation planning, and climate adaptation strategies.