Viral phylodynamics focuses on using sequence data to make inferences about the population dynamics of viral diseases. These inferences commonly include estimation of growth rates, reproduction numbers and times of most recent common ancestor. With few exceptions, existing phylodynamic inference approaches assume that all observed and ancestral viral genetic variation is fitness-neutral. This assumption is commonly violated, with a large body of analyses indicating that fitness varies substantially among genotypes circulating in viral populations. Here, we focus on fitness variation arising from deleterious mutations, asking whether incomplete purifying selection of deleterious mutations has the potential to bias phylodynamic inference. We use simulations of an exponentially growing population to explore how incomplete purifying selection distorts tree shape and shifts the distribution of mutations over trees. We find that incomplete purifying selection strongly shapes the distribution of mutations while only weakly impacting tree shape. Despite incomplete purifying selection shifting the distribution of deleterious mutations, we find little discernible bias in estimates of viral growth rates and times of the most recent common ancestor. Our results reassuringly indicate that existing phylodynamic inference approaches that assume neutrality may nevertheless yield accurate epidemiological estimates in the face of incomplete purifying selection. More work is needed to assess the robustness of these findings to alternative epidemiological parametrizations.This article is part of the theme issue ''"A mathematical theory of evolution": phylogenetic models dating back 100 years'.