Kazakhstan is recently experiencing an increase in drought trends. However, low-capacity probabilistic drought forecasts and poor dissemination have led to a drought crisis in 2021 that resulted in the loss of thousands of livestock. To improve drought forecasting accuracy, this study applies Machine Learning and Deep Learning (ML and DL) algorithms to capture the sequences of drought events using a non-contiguous drought analysis (NCDA). Precipitation, 2-m temperature, runoff, solar radiation, relative humidity, and evaporation were collected from the ERA5 database as input variables. Combinations of inputs were used to build ML models, including seven classifiers (Logistic, K-NN, Kernel SVM, Decision Tree, Random Forest, XGBoost, and GRU). The output events were defined by standardized precipitation index (SPI) and SPEI indicators as binary classes. Weekly time series from 1991 to 2021 for each cell were used to forecast a lead time from 1 week to 6 months. GRU provided 97–99% accuracy in more volatile regions while Random Forest and XGBoost showed 94–99% accuracy at a lead time of 6 months. The accuracy evaluation was based on the confusion matrix and F1 score to analyze the stage change capture. This study demonstrates the effectiveness of using ML and DL algorithms for drought forecasting, with potential applications for other regions.