The ongoing coronavirus disease 2019 pandemic, like other disasters or crises, can immensely influence visitors’ demand to visit affected destinations. The current study helps us better understand how this health crisis could affect the demand change from a micro-level perspective of small-scale tourist destinations. Based on the web search data from the Baidu Index, the present study adopts the Emeishan National Park in China as the study area and employs multiple methods to assess the spatial-temporal disparities in the impact of the coronavirus disease 2019 on domestic tourism demand. The main findings reveal that the demand changes during the observation period resemble a U-shaped curve along with the outbreak, spread, and control of the crisis, and such impacts exhibit different characteristics in the pre-event, prodromal, emergency, intermediate, and long-term recovery stages. During and after the pandemic, the short-distance market is the most vulnerable, but it presents the strongest resilience, while the medium- and long-distance markets are relatively less affected. Significant stratified heterogeneity in the tourism demand of domestic source markets also emerges before and after the crisis. Finally, some implications of promoting domestic tourism recovery in the post-pandemic era are discussed, and recommendations are made.