Yellow fever and dengue are viral infections that in urban centres are transmitted by the same arthropod vector, a mosquito of the genus Aedes. In order to estimate the risk of an epidemic of urban yellow fever in a dengue-infested area we calculated the threshold in the basic reproduction number, R0, of dengue, above which any single sylvatic yellow fever-infected individual will trigger an urban yellow fever epidemic. Specifically, we analysed the relationship between the extrinsic incubation period and the duration of viraemia, from which it is possible to define the R0 for dengue that would also suggest an outbreak potential for yellow fever. We also calculated the critical proportion of people to vaccinate against yellow fever in order to prevent an epidemic in a dengue-endemic area. The theory proposed is illustrated by the case of São Paulo State in southern Brazil, where dengue is endemic and the risk of urban yellow fever is already imminent.