To assess the impact of China's regional emergency logistics response capabilities on economic growth sustainability, this study develops a set of comprehensive indicators. It applies the entropy weight method combined with the TOPSIS method to evaluate these capabilities across regions. Based on panel data from 30 provinces in China from 2012 to 2021, this study employs panel models, panel quantile regression, and panel threshold models to analyze the impact of emergency logistics response capability on sustainable economic growth. By measuring the regional emergency logistics response capability and examining its effects on the sustainability of economic growth, this research provides foreign investors with a clearer understanding of the ability of different regions in China to handle unexpected public incidents. This, in turn, helps reduce investment uncertainty, mitigate certain risks, and offers valuable insights for enhancing the efficiency of international investments in China. Key findings are: (1) Since 2018, the establishment of the Ministry of Emergency Management has significantly improved China's regional emergency logistics capabilities, with the eastern region outperforming the central and western regions. (2) Enhancing China's emergency logistics response capability helps improve the sustainability level of economic growth. This reflects how China's emergency management departments can mitigate the adverse impacts of public emergencies on economic growth by transforming social logistics into emergency logistics. (3) As emergency response capabilities have strengthened, their impact on economic sustainability initially decreased but later increased.