In agroecosystems, drought is a critical climatic phenomenon that affects evapotranspiration and induces water stress in plants. The objective in this study was to characterize and forecast water stress in the Hyderabad region of India using artificial intelligence models. The monthly precipitation data for the period 1982–2021 was characterized by the standardized precipitation index (SPI) and modeled using the classical autoregressive integrated moving average (ARIMA) model and artificial intelligence (AI), i.e., artificial neural network (ANN) and support vector regression (SVR) model. The results show that on the short-term SPI3 time scale the studied region experienced extreme water deficit in 1983, 1992, 1993, 2007, 2015, and 2018, while on the mid-term SPI6 time scale, 1983, 1991, 2011, and 2016 were extremely dry. In addition, the prediction of drought at both SPI3 and SPI6 time scales by AI models outperformed the classical ARIMA models in both, training and validation data sets. Among applied models, the SVR model performed better than other models in modeling and predicting drought (confirmed by root mean square error—RMSE), while the Diebold–Mariano test confirmed that SVR output was significantly superior. A reduction in the prediction error of SVR by 48% and 32% (vs. ARIMA), and by 21% and 26% (vs. ANN) was observed in the test data sets for both SPI3 and SPI6 time scales. These results may be due to the ability of the SVR model to account for the nonlinear and complex patterns in the input data sets against the classical linear ARIMA model. These results may contribute to more sustainable and efficient management of water resources/stress in cropping systems.