Natural disasters pose serious threats to large urban areas, therefore understanding and predicting human movements is critical for evaluating a population’s vulnerability and resilience and developing plans for disaster evacuation, response and relief. However, only limited research has been conducted into the effect of natural disasters on human mobility. This study examines how natural disasters influence human mobility patterns in urban populations using individuals’ movement data collected from Twitter. We selected fifteen destructive cases across five types of natural disaster and analyzed the human movement data before, during, and after each event, comparing the perturbed and steady state movement data. The results suggest that the power-law can describe human mobility in most cases and that human mobility patterns observed in steady states are often correlated with those in perturbed states, highlighting their inherent resilience. However, the quantitative analysis shows that this resilience has its limits and can fail in more powerful natural disasters. The findings from this study will deepen our understanding of the interaction between urban dwellers and civil infrastructure, improve our ability to predict human movement patterns during natural disasters, and facilitate contingency planning by policymakers.