The reliable estimation of lag time and its association with meteorological drought is very important for early mitigation of hydrological drought. The relationship between meteorological and hydrological droughts is very complex because it depends on watershed characteristics as well as climatic factors. The objective of this study is to figure out probabilistic relationships of weekly lag time between the hydrological drought defined by Standardized Runoff Index (SRI) and the meteorological drought defined by Standardized Precipitation Index (SPI) and Standardized Evapotranspiration Index (SPEI) using a Bayesian network model. The results showed that the lag time varied spatially with the intensity of meteorological droughts. The results also revealed the probabilistic relationships that meteorological droughts with moderate intensity resulted in a higher probability of longer lag time, whereas meteorological droughts with severe intensity led to a lower probability of longer lag time. The probability of lag time also varied with meteorological drought indices; at the same intensity, the probability of lag time occurring is higher in the case of SPI and lower in the case of SPEI. These results will be very helpful for early mitigating hydrological drought hazard and making strategies to cope with losses from hydrological droughts.