While protective measures in response to infectious diseases may reduce the freedom of tourists (regarding their behaviors), few studies have documented the effects of destination protective measures on the self-protective behaviors of tourists. By applying the protection motivation theory, this study examines the effects of perceived destination protective supports on the social distancing intentions of tourists during the COVID-19 pandemic. The results reveal significant relationships among perceived destination support, coping appraisal, threat appraisal, and the social distancing intentions of tourists. Moreover, two cognitive appraisals—toward the pandemic—partially mediate the relationship between perceived destination support and social distancing intention, and this mediational process is ‘intervened’ with by social norms. This has implications on whether tourist destinations apply more rigorous social distancing polices during the COVID-19 pandemic, to enhance the coping confidence behaviors of tourists, without causing anxiety and fear, and to achieve the goal of enhancing tourists’ intentions to protect themselves.