We present a maximum likelihood (ML) analysis of the selection pressures that have shaped the evolution of the large (L) protein and the haemagglutinin (H) glycoprotein of measles virus (MV). A number of amino acid sites that have potentially been subject to adaptive evolution were identified in the H protein using sequences from every known genotype of MV. All but one of these putative positively selected sites reside within the ectodomain of the H protein, where they often show an association with positions of potential B-cell epitopes and sites known to interact with the CD46 receptor. This suggests that MV may be under pressure from the immune system, albeit relatively weakly, to alter sites within epitopes and hence evade the humoral immune response. The positive selection identified at amino acid 546 was shown to correlate with the passage history of MV isolates in Vero cells. We reveal that Vero cell passaging has the potential to introduce an artificial signal of adaptive evolution through selection for changes that increase affinity for the CD46 receptor.