Access to healthcare services is largely determined by socioeconomic factors, with economically well-off individuals obtaining healthcare services more efficiently than those who are disadvantaged. This paper aims to assess the effects of socioeconomic and other related factors on access to healthcare facilities in the City of Tshwane, South Africa, during the COVID-19 pandemic. Data were sourced from the Gauteng City-Region Observatory (GCRO) quality of life survey (2020/2021). Multivariate logistic regression was applied. Results showed that 66.3% of the respondents reported that they had access to public healthcare facilities within their area. Furthermore, results showed that those who lived in informal houses were significantly (OR = 0.55, 95% CI [0.37–0.80], p < 0.01) less likely to report that they had access to public healthcare facilities in their area compared to those who lived in formal houses. More efforts need to be undertaken to ensure that all citizens have access to public healthcare facilities, especially among those who are disadvantaged, such as informal dwellers. In addition, future research should encompass locality in relation to the factors that affect access to public healthcare facilities, especially during pandemics such as the COVID-19 pandemic, in order to have geographically targeted interventions.