More than 15 years after the first human cases of influenza A/H5N1 in Hong Kong, the world remains at risk for an H5N1 pandemic. Preparedness activities have focused on antiviral stockpiling and distribution, development of a human H5N1 vaccine, operationalizing screening and social distancing policies, and other non-pharmaceutical interventions. The planning of these interventions has been done in an attempt to lessen the cumulative mortality resulting from a hypothetical H5N1 pandemic. In this theoretical study, we consider the natural limitations on an H5N1 pandemic's mortality imposed by the virus' epidemiological–evolutionary constraints. Evolutionary theory dictates that pathogens should evolve to be relatively benign, depending on the magnitude of the correlation between a pathogen's virulence and its transmissibility. Because the case fatality of H5N1 infections in humans is currently 60 per cent, it is doubtful that the current viruses are close to their evolutionary optimum for transmission among humans. To describe the dynamics of virulence evolution during an H5N1 pandemic, we build a mathematical model based on the patterns of clinical progression in past H5N1 cases. Using both a deterministic model and a stochastic individual-based simulation, we describe (i) the drivers of evolutionary dynamics during an H5N1 pandemic, (ii) the range of case fatalities for which H5N1 viruses can successfully cause outbreaks in humans, and (iii) the effects of different kinds of social distancing on virulence evolution. We discuss two main epidemiological–evolutionary features of this system (i) the delaying or slowing of an epidemic which results in a majority of hosts experiencing an attenuated virulence phenotype and (ii) the strong evolutionary pressure for lower virulence experienced by the virus during a period of intense social distancing.