One of the commonest explanations for the evolutionary radiation of animals during the Cambrian and Ordovician periods (about 541 to 443 million years ago) is the predation hypothesis. According to this widely cited but untested idea, the first rise of predatory animals would have accelerated evolution, and so diversification, by increasing natural selection on preys and starting predator-prey coevolutionary arms races. This predation-diversification hypothesis is here tested for the first time for the Cambrian—Ordovician radiation, by comparing the pace of origination of marine invertebrates and the dynamics of the predator ratio in fossil communities, at the local scale and genus level, focusing on the open shelf habitat (reefs excluded). Overall, origination rates decreased whereas the median predator ratio first increased up to a maximum at the middle—late Cambrian and then decreased more or less gradually during the Ordovician. Time-series analysis, using data differencing and detrending, shows that there is no positive correlation between origination rate and synchronic predator ratio over the Cambrian and Ordovician. Thus, the results do not provide evidence of any acceleration of origination rate driven by the rise of predation. Predatory animals might have contributed to the start of the Cambrian—Ordovician radiation by promoting defensive exoskeletons and infaunal lifestyles, but the results suggest they did not facilitate diversification in any other way.