Drought is one of the detrimental climatic factors that affects the productivity and quality of tea by limiting the growth and development of the plants. The aim of this research was to determine drought stress in tea estates using a remote sensing technique with the standardized precipitation index (SPI). Landsat 8 OLI/TIRS images were processed to measure the land surface temperature (LST) and soil moisture index (SMI). Maps for the normalized difference moisture index (NDMI), normalized difference vegetation index (NDVI), and leaf area index (LAI), as well as yield maps, were developed from Sentinel-2 satellite images. The drought frequency was calculated from the classification of droughts utilizing the SPI. The results of this study show that the drought frequency for the Sylhet station was 38.46% for near-normal, 35.90% for normal, and 25.64% for moderately dry months. In contrast, the Sreemangal station demonstrated frequencies of 28.21%, 41.02%, and 30.77% for near-normal, normal, and moderately dry months, respectively. The correlation coefficients between the SMI and NDMI were 0.84, 0.77, and 0.79 for the drought periods of 2018–2019, 2019–2020 and 2020–2021, respectively, indicating a strong relationship between soil and plant canopy moisture. The results of yield prediction with respect to drought stress in tea estates demonstrate that 61%, 60%, and 60% of estates in the study area had lower yields than the actual yield during the drought period, which accounted for 7.72%, 11.92%, and 12.52% yield losses in 2018, 2019, and 2020, respectively. This research suggests that satellite remote sensing with the SPI could be a valuable tool for land use planners, policy makers, and scientists to measure drought stress in tea estates.