Digital proximity tracing apps have been released to mitigate the transmission of SARS-CoV-2, the virus known to cause COVID-19. However, it remains unclear how the acceptance and uptake of these apps can be improved. This study aimed to investigate the coverage of the SwissCovid app and the reasons for its nonuse in Switzerland during a period of increasing incidence of COVID-19 cases. We collected data between September 28 and October 8, 2020, via a nationwide online panel survey (COVID-19 Social Monitor, N=1511). We examined sociodemographic and behavioral factors associated with app use by using multivariable logistic regression, whereas reasons for app nonuse were analyzed descriptively. Overall, 46.5% (703/1511) of the survey participants reported they used the SwissCovid app, which was an increase from 43.9% (662/1508) reported in the previous study wave conducted in July 2020. A higher monthly household income (ie, income >CHF 10,000 or >US $11,000 vs income ≤CHF 6000 or <US $6600 reference: odds ratio OR 1.92, 95% CI 1.40-2.64), more frequent internet use (ie, daily reference vs less than weekly: OR 0.37, 95% CI 0.16-0.85), better adherence to recommendations for wearing masks (ie, always or most of the time reference vs rarely or never: OR 0.28, 95% CI 0.15-0.52), and nonsmoker status (OR 1.32, 95% CI 1.01-1.71) were associated with an increased likelihood for app uptake. Citizenship status (ie, non-Swiss citizenship vs. Swiss reference: OR 0.61, 95% CI 0.43-0.87), and language region (French vs Swiss German reference: OR 0.61, 95% CI 0.46-0.80) were associated with a lower likelihood for app uptake. Further analysis in a randomly selected subsample (n=712) with more detailed information showed that higher levels of trust in government and health authorities were also associated with a higher likelihood for app uptake (ie, high vs low reference trust: OR 3.13, 95% CI 1.58-6.22). The most frequent reasons for app nonuse were lack of perceived benefit of using the app (297/808, 36.8%), followed by the lack of a compatible phone (184/808, 22.8%), and privacy concerns (181/808, 22.4%). Eliminating technical hurdles and communicating the benefits of digital proximity tracing apps are crucial to promote further uptake and adherence of such apps and, ultimately, enhance their effectiveness to aid pandemic mitigation strategies.