Emerging evidence suggests a possible link between exposure to household air pollution (HAP) from a reliance on polluting solid fuels (SFs) (e.g., wood and charcoal) for cooking and high blood pressure. As part of the CLEAN-Air(Africa) project, we measured the blood pressure among 350 cooks in Obuasi Municipality, Ghana after 24 h exposure to particulate matter (PM2.5) from the combustion of either solid fuels (n = 35) or liquefied petroleum gas (LPG) (n = 35). Multinomial regression models were used to describe the relationship between different stages of blood pressure (mmHg) and the respondents’ main fuel type used, adjusting for key covariates. A linear regression model was used to describe the relationship between personal exposure to PM2.5 and the respondent’s systolic as well as diastolic blood pressure, adjusting for key covariates. Blood pressure was higher in cooks using SFs for cooking than in those using LPG. A significant exposure–response relationship was not observed between increasing exposure to PM2.5 and increasing blood pressure (systolic: β = −2.42, 95% CI: −8.65, 3.80, p-value = 0.438, and diastolic: β = −0.32, 95% CI: −5.09; 4.45, p-value = 0.893).