The low-lying Vietnamese Mekong Delta (VMD) is a key agricultural production landscape increasingly threatened by anthropogenic stresses and climate change. Among the different threats, droughts caused by extreme events, climate change and upstream developments, affect the delta the most. This paper explores the relationship between the intensity, duration, and frequency of meteorological droughts and hydrological droughts using a range of indices. We used monthly rainfall and stream flow data for the period 1992–2021 to calculate the Standardized Precipitation Index (SPI), the Reconnaissance Drought Index (RDI), and the streamflow drought Index (SDI) for different time intervals. We found no observed time lag, and a strong correlation coefficient between upstream hydrological and downstream meteorological drought events assessed over long-term scales (i.e., 12-months). This is true for all downstream sites, except Ben Tre City. Hydrological drought events onset lagged 5–6-, 6-, and 3–4-month behind meteorological droughts at mid- and shorter assessment time scales (9-, 6-, 3-month). The average correlation coefficients between hydrological indices and meteorological indices at 9–3-month time scales ranged from moderate to weak. These findings shed light and advance the understanding of the progression of meteorological to hydrological droughts in the VMD. Our results aid the regional understanding of drought onset and the causative mechanisms at work, which is important for both medium- and long-term drought forecasting and adaptation planning.