The effect of the Cretaceous–Palaeogene (K–Pg) mass extinction on the evolution of many groups, including placental mammals, has been hotly debated. The fossil record suggests a sudden adaptive radiation of placentals immediately after the event, but several recent quantitative analyses have reconstructed no significant increase in either clade origination rates or rates of character evolution in the Palaeocene. Here we use stochastic methods to date a recent phylogenetic analysis of Cretaceous and Palaeocene mammals and show that Placentalia likely originated in the Late Cretaceous, but that most intraordinal diversification occurred during the earliest Palaeocene. This analysis reconstructs fewer than 10 placental mammal lineages crossing the K–Pg boundary. Moreover, we show that rates of morphological evolution in the 5 Myr interval immediately after the K–Pg mass extinction are three times higher than background rates during the Cretaceous. These results suggest that the K–Pg mass extinction had a marked impact on placental mammal diversification, supporting the view that an evolutionary radiation occurred as placental lineages invaded new ecological niches during the Early Palaeocene.