Groundwater is very important for human productivity and daily life, hydrological cycle regulation, and ecosystem stability. However, due to the complex mechanisms of groundwater drought, the spatial and temporal variations of groundwater drought and its driving mechanisms are still not fully understood, especially in Indochina Peninsula. In this work, we used a reconstructed long-term terrestrial water storage dataset from the Gravity Recovery and Climate Experiment (GRACE) emission and a GRACE-based groundwater drought index to investigate the spatial and temporal characteristics of groundwater drought during 1979–2020 in the Indochina Peninsula. The possible teleconnection mechanisms between groundwater drought and the Indian Ocean Dipole (IOD), El Niño-Southern Oscillation (ENSO), and El Niño Modoki (ENSO_M) were also investigated using cross wavelet transform method. The results show that groundwater drought worsens significantly during 1979–2020, and becomes much more frequent and intensified after 2000 in the southern Indochina Peninsula. Both univariate and bivariate (logic ‘or’ and ‘and’) return periods for duration, severity, and peak of groundwater drought are short in the southern Indochina Peninsula, and thus the risk of groundwater drought is high. The IOD, ENSO, and ENSO_M can reduce the intensity of groundwater drought to a certain extent during the warm phases, but only ENSO_M tends to significantly exacerbate the intensity of groundwater drought during the cold phases in the southern Indochina Peninsula. The variations in groundwater drought are dominated by ENSO_M, and are also coupled influenced by the IOD and ENSO in the southern Indochina Peninsula. The results provide valuable information for the sustainable ecological environment and socioeconomic development, especially development of groundwater drought early warning and prediction models in the Indochina Peninsula.