Introduction Access to medicines is a challenge, especially in developing countries, highlighting the need of population-based research to evaluate access and related factors. Objective This study aimed to assess access to medicines and identify associated factors using data from the 2019 Brazilian National Health Survey (PNS). Methods This population-based cross-sectional study used data from the 2019 PNS and considered access to prescription medicines as the primary outcome. The sample included 24,753 individuals aged 15 years or older who looked for medical care in the last 15 days and received a medicine prescription. Andersen’s behavioral model was used to select independent variables. After descriptive analysis, a multinomial logistic regression multilevel analysis was performed using the independent variables with a significance level lower than 0.20 in the bivariate analysis. Results The lowest chances of getting access to medicines were observed in individuals aged between 40 and 59 years, women, with complete middle and high school, with lower-income families, who attended public services, with worse self-assessed health, and those who looked for health care for disease prevention and health promotion. Conclusions Access to medicines among the Brazilian population is associated with social, economic, and health perception factors. Our findings may update and guide the development of public policies on medication and pharmaceutical care, facilitating medication purchases by the care user and promoting health equity.