Brazil is the only country in Latin America that has adopted a national health system. This causes differences in access to health among Latin American countries and induces noticeable migration to Brazilian regions to seek healthcare. This phenomenon has led to difficulties in the control and elimination of diseases related to poverty, such as leprosy. The aim of this study was to evaluate social determinants and their relationship with the risk of leprosy, as well as to examine the temporal trend of its occurrence in a Brazilian municipality located on the tri-border area between Brazil, Paraguay and Argentina. This ecological study investigated newly-diagnosed cases of leprosy between 2003 and 2015. Exploratory analysis of the data was performed through descriptive statistics. For spatial analysis, geocoding of the data was performed using spatial scan statistic techniques to obtain the Relative Risk (RR) for each census tract, with their respective 95% confidence intervals calculated. The Bivariate Moran I test, Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models were applied to analyze the spatial relationships of social determinants and leprosy risk. The temporal trend of the annual coefficient of new cases was obtained through the Prais-Winsten regression. A standard error of 5% was considered statistically significant (p < 0.05). Of the 840 new cases identified in the study, there was a predominance of females (n = 427, 50.8%), of white race/color (n = 685, 81.6%), age range 15 to 59 years (n = 624, 74.3%), and incomplete elementary education (n = 504, 60.0%). The results obtained from multivariate analysis revealed that the proportion of households with monthly nominal household income per capita greater than 1 minimum wage (β = 0.025, p = 0.036) and people of brown race (β = -0.101, p = 0.024) were statistically-significantly associated with risk of illness due to leprosy. These results also confirmed that social determinants and risk of leprosy were significantly spatially non-stationary. Regarding the temporal trend, a decrease of 4% (95% CI [-0.053, -0.033], p = 0.000) per year was observed in the rate of detection of new cases of leprosy. The social determinants income and race/color were associated with the risk of leprosy. The study’s highlighting of these social determinants can contribute to the development of public policies directed toward the elimination of leprosy in the border region. The World Health Organization considers Brazil to be a priority country for the control of leprosy. This is determined by the high rates of prevalence, detection of new cases and proportion of cases in females, proportion of cases in children, and people with degree of incapacity II. Moreover, Brazil has been unable to achieve the target of one case per 10,000 inhabitants, despite efforts to eliminate the disease. Elimination and control become even more complex challenges in border regions if we consider the heavy flow of people between countries and the resulting overload for the local health system. Thus, this study aimed to identify the risk of leprosy and its social determinants, as well as to investigate the temporal trend of the disease in a region with a triple border, connecting Brazil, Paraguay and Argentina. We identified 840 new cases in the study; there was a predominance of women (n = 427, 50.8%), of white race/color (n = 685, 81.6%), age range 15 to 59 years (n = 624, 74.3%), with incomplete elementary education (n = 504, 60.0%). The social determinants income and race/color were associated with the risk of leprosy. The results may contribute to the planning of actions in health for border regions.