Hydrodynamic instability of vehicles in urban flooding always leads to a serious loss of people's life and property all over the world. Thus it is vital to formulate the safety criterion of the vehicle exposed to urban floodwater. In this study, an explicit expression for the incipient velocity of a flooded vehicle concerning water depth is derived based on the Shannon and Tsallis entropy concepts. This entropy-based expression can mimic the decaying trend of the incipient velocity with water depth from shallow water to deep water. Furthermore, a comparison with five experimental datasets regarding the critical instability condition of flooded vehicles shows its validity with a high correlation coefficient and a low relative bias. Sensitivity test results of the entropic model to some parameters, including the friction coefficient, the drag coefficient, densities of the vehicle and surrounding fluid, and length and height of the vehicle, are found to be consistent with our qualitative understandings regarding the physical mechanism of hydrodynamic instability of the flooded vehicle. Taking two types of vehicles popular in China as an example: Audi Q7 passenger car and Ford V348 ambulance, this study illustrates the vulnerability degree zoning of flooded vehicles, which could be referred to by administrators and stakeholders for flood hazard evaluation and flood emergency management. With an increasing floodwater velocity and a surging water level, the safety of the flooded vehicle is threatened, and more protective measures are needed. This study indicates the potential of the entropy-based method as a good addition to existing empirical/semi-empirical models for characterizing the instability threshold of parking vehicles on a road or street in urban flooding.