Science communication in natural disasters is important to society but rarely informed by quantitative analysis of website traffic patterns. Analysis of science website traffic during the 2010–2012 Canterbury earthquake sequence in New Zealand reveals near‐instantaneous traffic surges after strong earthquakes followed by heavy‐tailed power‐law temporal decay consistent with Omori law for aftershocks. Traffic perturbations scale with earthquake magnitude and population exposure to strong shaking. Traffic also increases in response to public communications by the affiliated website operator. Website traffic decays with increasing seismic sequence duration but is ultimately sustained at levels 800%–1400% larger than pre‐event traffic, revealing sustained public utilization of science websites that outlast the duration of the associated natural disaster. Science websites with diverse sources and content exhibit similarly scaled traffic volume patterns. This study provides a clear, quantitatively justified motive for scientists of all affiliations to prioritize timely science communication with the public following time‐critical natural phenomena and disasters. Science website traffic for other natural disasters, including volcanic eruptions, cyclones, heatwaves, typhoons, and bushfires are similarly fit by power laws.