Influenza pandemics can emerge unexpectedly and wreak global devastation. However, each of the six pandemics since 1889 emerged in the Northern Hemisphere just after the flu season, suggesting that pandemic timing may be predictable. Using a stochastic model fit to seasonal flu surveillance data from the United States, we find that seasonal flu leaves a transient wake of heterosubtypic immunity that impedes the emergence of novel flu viruses. This refractory period provides a simple explanation for not only the spring-summer timing of historical pandemics, but also early increases in pandemic severity and multiple waves of transmission. Thus, pandemic risk may be seasonal and predictable, with the accuracy of pre-pandemic and real-time risk assessments hinging on reliable seasonal influenza surveillance and precise estimates of the breadth and duration of heterosubtypic immunity.