We propose a new theory of systemic risk based on Knightian uncertainty (or "ambiguity"). We show that, due to uncertainty aversion, beliefs on future asset returns are endogenous, and bad news on one asset class induces investors to be more pessimistic about other asset classes as well. This means that idiosyncratic risk can create contagion and snowball into systemic risk. Furthermore, in a Diamond and Dybvig (1983) setting, we show that, surprisingly, uncertainty aversion causes investors to be less prone to run individual banks, but runs will be systemic. In addition, we show that bank runs are associated with stock market crashes and flight to quality. Finally, we argue that increasing uncertainty makes the financial system more fragile and more prone to crises. We conclude with implications for the current public policy debate on the management of financial crisis.