Non-pharmacological measures, such as hand hygiene and face mask use, continue to play an important role in the fight against the COVID-19 pandemic. However, there is a paucity of studies on the adherence to these measures among students in Bhutan. Therefore, we aimed to investigate hand hygiene and face mask-wearing behaviours, as well as their associated factors, among the students of Mongar Higher Secondary School, Bhutan. We conducted a cross-sectional study amongst the students of Mongar Higher Secondary School in Bhutan. The students self-answered the questionnaire on web-based Google Forms. Multivariable logistic regression for good hand washing and face mask use was conducted in order to identify statistically significant socio-demographic covariates. The correlation between hand hygiene and mask use was investigated using Pearson’s correlation coefficient. A total of 533 students completed the survey questionnaire, 52.9% (282) of whom were female students. Facebook (44.3%, 236) and TV (35.5%, 189) were the two most popular sources of information on COVID-19 prevention and control. Good (scores of ≥80% of total scores) hand hygiene and face mask use were reported in 33.6% (179) and 22.1% (118) of students. In multivariable logistic regression, male students presented 79% (adjusted odds ratio [AOR] = 1.79, 95% confidence interval [CI] = 1.23−2.613) odds of engaging in good hand hygiene, compared to female students. Compared to grade 9, those in grade 10 were 60% (AOR = 0.4, 95% CI 0.158−0.998) less likely to engage in good hand hygiene. Boarding students presented 68% (AOR = 1.68, 95% CI 1.001, 2.813) higher odds of wearing a face mask compared to day students. There was a significant positive correlation between good hand hygiene and face mask use (r = 0.3671, p-value < 0.001). Good hand hygiene and face mask use were reported in less than one-third of the study participants. It is recommended to continue educating students on good hand hygiene and face mask use through popular information sources.