Comparing to data in patients with severe coronavirus diseases 2019 (COVID-19), there are few studies on the prevalence anxiety and/or depression in patients with asymptomatic or mildly symptomatic COVID-19. We investigated the clinical characteristics and the prevalence of anxiety and/or depression among asymptomatic or mildly symptomatic patients with COVID-19 and monitored their mental health using an online assessment. An online survey for monitoring and assessing the mental health of patients with COVID-19 using a mobile phone was conducted. We used the Hospital Anxiety and Depression Scale to measure anxiety and/or depression levels. Of the 234 patients, 66 patients were asymptomatic (28.2%), while the remaining 168 patients were mildly symptomatic. The prevalence of anosmia (p = 0.001) and ageusia (p = 0.008) significantly decreased with the increasing age. In addition, 19.8% and 14.0% patients had anxiety and/or depression in the first survey, and one week after the first survey, respectively. Compared to patients without anxiety and/or depression, those with anxiety and/or depression had a longer quarantine duration. We found that anomia and ageusia were relatively common in the young age group. Furthermore, one-fifth asymptomatic or mildly symptomatic patients with COVID-19 had anxiety and/or depression.