Drought is a complex environmental hazard to ecosystems and society. Decision-making on drought management options requires evaluating and predicting the extremity of future drought events. In this regard, quantifiable indices such as the standardized precipitation index (SPI), the standardized precipitation evapotranspiration index (SPEI), and the standardized streamflow index (SSI) have been commonly used to characterize meteorological and hydrological drought. In general, the estimation and prediction of the indices require an extensive range of precipitation (SPI and SPEI) and discharge (SSI) datasets in space and time domains. However, there is a challenge for long-term and spatially extensive data availability, leading to the insufficiency of data in estimating drought indices. In this regard, this study uses satellite precipitation data to estimate and predict the drought indices. SPI values were calculated from the precipitation data obtained from the Centre for Hydrometeorology and Remote Sensing (CHRS) data portal for a study water basin. This study employs a hydrological model for calculating discharge and drought in the overall basin. It uses random forest (RF) and support vector regression (SVR) as machine learning models for SSI prediction for time scales of 1- and 3-month periods, which are widely used for establishing interactions between predictors and predictands that are both linear and non-linear. This study aims to evaluate drought severity variation in the overall basin using the hydrological model and compare this result with the machine learning model’s results. The results from the prediction model, hydrological model, and the station data show better correlation. The coefficients of determination obtained for 1-month SSI are 0.842 and 0.696, and those for the 3-month SSI are 0.919 and 0.862 in the RF and SVR models, respectively. These results also revealed more precise predictions of machine learning models in the longer duration as compared to the shorter one, with the better prediction result being from the SVR model. The hydrological model-evaluated SSI has 0.885 and 0.826 coefficients of determination for the 1- and 3-month time durations, respectively. The results and discussion in this research will aid planners and decision-makers in managing hydrological droughts in basins.