The success of public health measures for controlling the coronavirus disease 2019 (COVID-19) pandemic relies on population compliance. We analyzed compliance with social distancing and its associations with mental health. The Hong Kong COVID-19 Health Information Survey was conducted from 9–23 April 2020 on 1501 adults randomly sampled for landline telephone interviews (n = 500) and online surveys (n = 1001). Compliance with social distancing and staying-at-home, stress (Perceived Stress Scale-4), anxiety (General Anxiety Disorders-2), and depressive symptoms (Patient Health Questionnaire-2) were collected. The associations between mental health symptoms and compliance were examined by multivariable regression models. Of the 1501 respondents (52.5% female, 72.3% aged 18–59 years), 74.2%, 72.7%, and 59.7% reported avoiding going out, going to crowded places, and attending social gatherings of more than four people, respectively. Most respondents had stayed-at-home for at least four of the past seven days (58.4%; mean 4.12, Standard Deviation 2.05). Adoption, perceived effectiveness, and perceived compliance with social distancing were associated with lower stress levels and less anxiety and depressive symptoms (all p < 0.01). However, more days stayed-at-home were associated with more depressive symptoms (adjusted Odds Ratio 1.09; 95%Confidence Interval 1.00, 1.18). The long-term psychological impact in relation to social distancing and staying-at-home requires further investigation.