Bangladesh is experiencing a rapid increase in hypertension prevalence, particularly in socio-economically disadvantaged communities. The higher use of solid fuel in these communities could be one of the significant factors contributing to this trend, but evidence supporting this hypothesis is limited in Bangladesh. Therefore, this study aims to investigate the associations of household solid fuel use and its exposure level with systolic and diastolic blood pressure (DBP) and hypertension. We analysed 7,320 women’s data from 2017/18 Bangladesh Demographic and Health Survey. We considered three outcome variables: (i) systolic blood pressure (BP) (continuous response), (ii) DBP (continuous response), and (iii) hypertension status (yes, no). Our primary exposures of interest were fuel type (clean vs solid) and the potential level of household air pollution exposure through solid fuel use (unexposed, moderately exposed, and highly exposed). We used a multilevel mixed-effects Poisson regression model with robust variance to determine association between exposure and outcome variables while adjusting for confounders. Of the total respondents analysed, approximately 82% used solid fuel for cooking. The age-standardised prevalence of hypertension was 28%. Respondents using solid fuel were found to be 1.44 times (95% confidence interval [CI], 1.04–1.89) more likely to develop hypertension compared to clean fuel users. Compared to women using clean fuel, the likelihood of hypertension was found to be 1.61 times (95% CI, 1.07–2.20) higher among the moderately exposed group and 1.80 times (95% CI, 1.27–2.32) higher among the highly exposed group. Similar associations were reported for systolic and DBP. The use of solid fuel increases the risk of becoming hypertensive and elevates systolic and DBP. Policies and programmes are necessary to increase awareness of the adverse effects of solid fuel use on health, including hypertension. Efforts should be made to reduce solid fuel use and ensure proper ventilation systems in households where solid fuel is used.