Daily variation in human mobility modulates the speed and severity of emerging outbreaks, yet most epidemiological studies assume static contact patterns. With a highly mobile population exceeding 24 million people, Shanghai, China is a transportation hub at high risk for the importation and subsequent global propagation of infectious diseases. Here, we use a dynamic metapopulation model informed by hourly transit data for Shanghai to estimate epidemic risks across thousands of outbreak scenarios. We find that the rate of initial epidemic growth varies by more than twenty-fold, depending on the hour and neighborhood of disease introduction. The riskiest introductions are those occurring close to the city center and on Fridays--which bridge weekday and weekend transit patterns and thereby connect otherwise disconnected portions of the population. The identification of these spatio-temporal hotspots can inform more efficient targets for sentinel surveillance and strategies for mitigating transmission.