Vietnam, one of the three leading rice producers globally, has recently seen an increased threat to its rice production emanating from climate extremes (floods and droughts). Understanding spatio-temporal variability in precipitation and soil moisture is essential for policy formulations to adapt and cope with the impacts of climate extremes on rice production in Vietnam. Adopting a higher-order statistical method of independent component analysis (ICA), this study explores the spatio-temporal variability in the Climate Hazards Group InfraRed Precipitation Station’s (CHIRPS) precipitation and the Global Land Data Assimilation System’s (GLDAS) soil moisture products. The results indicate an agreement between monthly CHIRPS precipitation and monthly GLDAS soil moisture with the wetter period over the southern and South Central Coast areas that is latter than that over the northern and North Central Coast areas. However, the spatial patterns of annual mean precipitation and soil moisture disagree, likely due to factors other than precipitation affecting the amount of moisture in the soil layers, e.g., temperature, irrigation, and drainage systems, which are inconsistent between areas. The CHIRPS Standardized Precipitation Index (SPI) is useful in capturing climate extremes, and the GLDAS Standardized Soil Moisture Index (SSI) is useful in identifying the influences of climate extremes on rice production in Vietnam. During the 2016–2018 period, there existed a reduction in the residual rice yield that was consistent with a decrease in soil moisture during the same time period.