Dengue fever is a mosquito-borne virus that infects 50-100 million people each year. Of these infections, 200,000-500,000 occur as the severe, life-threatening form of the disease, dengue haemorrhagic fever (DHF). Large, unanticipated epidemics of DHF often overwhelm health systems. An understanding of the spatial-temporal pattern of DHF incidence would aid the allocation of resources to combat these epidemics. Here we examine the spatial-temporal dynamics of DHF incidence in a data set describing 850,000 infections occurring in 72 provinces of Thailand during the period 1983 to 1997. We use the method of empirical mode decomposition to show the existence of a spatial-temporal travelling wave in the incidence of DHF. We observe this wave in a three-year periodic component of variance, which is thought to reflect host-pathogen population dynamics. The wave emanates from Bangkok, the largest city in Thailand, moving radially at a speed of 148 km per month. This finding provides an important starting point for detecting and characterizing the key processes that contribute to the spatial-temporal dynamics of DHF in Thailand.