We measured the health resource agglomeration capacities of 31 Chinese provinces (or municipalities) in 2004–2018 based on the entropy weight method. Using a modified spatial gravity model, we constructed and analyzed the spatial correlation network of these health resource agglomeration capacities and their influencing factors through social network analysis. We found that: (i) China’s health resource agglomeration capacity had a gradual strengthening trend, with capacity weakening from east to west (strongest in the eastern region, second strongest in the central region, and weakest in the western region). (ii) The spatial network of such capacities became more densely connected, and the network density and level (efficiency) showed an upward (downward) trend. (iii) In terms of centrality, the high-ranking provinces (or municipalities) were Beijing, Shanghai, Jiangsu, Zhejiang, Guangdong, Shandong, Hunan, Hubei, Fujian, Anhui, Jiangxi, and Tianjin, while the low-ranking were Tibet, Qinghai, Gansu, Ningxia, Inner Mongolia, Heilongjiang, Yunnan, Guizhou, Xinjiang, Hainan, Shaanxi, and Shanxi. (iv) Block 1 (eight provinces or municipalities), including Beijing, Tianjin, and Hebei, had a “net spillover” effect in the spatial network of health resource agglomeration capacities; Block 2, (seven provinces or municipalities), including Shanghai, Jiangsu, and Zhejiang, had a “bidirectional spillover” effect in the spatial network; Block 3 (seven provinces or municipalities), including Anhui, Hubei, and Hunan, had a “mediator” effect in the network; and Block 4, (nine provinces or municipalities), including Sichuan, Guizhou, and Tibet, had a “net beneficial” effect in the network. (v) The economic development, urbanization wage, and financial health expenditure levels, and population size had significant positive correlations with the spatial network of health resource agglomeration capacities. Policy recommendations to enhance the radiating role of health resources in core provinces (or municipalities), rationally allocate health resources, and transform ideas to support public health resource services were provided.