This paper investigates the associations between institution trust and public response to the COVID-19 outbreak. An Internet-based, cross-sectional survey was administered on January 29, 2020 to the epicenter Hubei province, China. A total of 4,393 adults who ≥18 years of age and residing or working in the province of Hubei were included in the study. The majority of the participants expressed a higher level of trust in the information and preventive instructions provided by the central government than by the local government. Being under quarantine (adjusted odds ratio (OR) = 2.35, 95% confidence interval (CI) 1.80–3.08) and having a high institutional trust score (OR = 2.23, 95% CI 1.96–2.53) were both strong and significant determinants of higher preventive behavior scores. The majority of study participants (85.7%, n = 3,640) reported that they would seek hospital treatment if they suspected themselves to have been infected with COVID-19. Few of the participants from Wuhan (16.6%, n = 475) and those participants who were under quarantine (13.8%, n = 550) expressed an unwillingness to seek hospital treatment. Institutional trust is an important factor influencing adequate preventive behavior and seeking formal medical care during an outbreak.