Animal-like multicellular fossils appeared towards the end of the Precambrian, followed by a rapid increase in the abundance and diversity of fossils during the Early Cambrian period, an event also known as the 'Cambrian explosion'. Changes in the environmental conditions at the Precambrian/Cambrian transition (about 542 Myr ago) have been suggested as a possible explanation for this event, but are still a matter of debate. Here we report molybdenum isotope signatures of black shales from two stratigraphically correlated sample sets with a depositional age of around 542 Myr. We find a transient molybdenum isotope signal immediately after the Precambrian/Cambrian transition. Using a box model of the oceanic molybdenum cycle, we find that intense upwelling of hydrogen sulphide-rich deep ocean water best explains the observed Early Cambrian molybdenum isotope signal. Our findings suggest that the Early Cambrian animal radiation may have been triggered by a major change in ocean circulation, terminating a long period during which the Proterozoic ocean was stratified, with sulphidic deep water.