Background Evidence about the impact of the COVID-19 pandemic on the mental health of specific subpopulations, such as university students, is needed as communities prepare for future waves. Aims To study the association of proximity of COVID-19 with symptoms of anxiety and depression in university students. Method This trend study analysed weekly cross-sectional surveys of probabilistic samples of students from the University of British Columbia for 13 weeks, through the first wave of COVID-19. The main variable assessed was propinquity of COVID-19, defined as ‘knowing someone who tested positive for COVID-19’, which was specified at different levels: knowing someone anywhere globally, in Canada, in Vancouver, in their course or at home. Proximity was included in multivariable linear regressions to assess its association with primary outcomes, including 30-day symptoms of anxiety and/or depression. Results Of 1388 respondents (adjusted response rate of 50%), 5.6% knew someone with COVID-19 in Vancouver, 0.8% in their course and 0.3% at home. Ten percent were overwhelmed and unable to access help. Knowing someone in Vancouver was associated with an 11-percentage-point increase in the probability of 30-day anxiety symptoms (s.e. 0.05, P ≤ 0.05), moderated by gender, with a significant interaction of the exposure and being female (coefficient −20, s.e. 0.09, P ≤ 0.05). No association was found with depressive symptoms. Conclusions Propinquity of COVID-19 cases may increase the likelihood of anxiety symptoms in students, particularly among men. Most students reported coping well, but additional support is needed for an emotionally overwhelmed minority who report being unable to access help.