Socioeconomic, ethnic and gender disparities in Chronic Obstructive Pulmonary Disease (COPD) risk are well established but no studies have applied multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) within an intersectional framework to study this outcome. We study individuals at the first level of analysis and combinations of multiple social and demographic categorizations (i.e., intersectional strata) at the second level of analysis. Here we used MAIHDA to assess to what extent individual differences in the propensity of developing COPD are at the intersectional strata level. We also used MAIHDA to determine the degree of similarity in COPD incidence of individuals in the same intersectional stratum. This leads to an improved understanding of risk heterogeneity and of the social dynamics driving socioeconomic and demographic disparities in COPD incidence. Using data from 2,445,501 residents in Sweden aged 45–65, we constructed 96 intersectional strata combining categories of age, gender, income, education, civil- and migration status. The incidences of COPD ranged from 0.02% for young, native males with high income and high education who cohabited to 0.98% for older native females with low income and low education who lived alone. We calculated the intra-class correlation coefficient (ICC) that informs on the discriminatory accuracy of the categorizations. In a model that conflated additive and interaction effects, the ICC was good (20.0%). In contrast, in a model that measured only interaction effects, the ICC was poor (1.1%) suggesting that most of the observed differences in COPD incidence across strata are due to the main effects of the categories used to construct the intersectional matrix while only a minor share of the differences are attributable to intersectional interactions. We found conclusive interaction effects. The intersectional MAIHDA approach offers improved information to guide public health policies in COPD prevention, and such policies should adopt an intersectional perspective.