Background Unlike developed countries, higher socioeconomic status (SES-education, and wealth) is associated with hypertension in low and middle-income countries (LMICs) with limited evidence. We examined the associations between SES and hypertension in Nepal and the extent to which these associations vary by sex and urbanity. The body mass index (BMI) was examined as a secondary outcome and assessed as a potential mediator. Materials and methods We analyzed the latest Nepal Demographic and Health Survey data (N = 13,436) collected between June 2016 and January 2017, using a multistage stratified sampling technique. Participants aged 15 years or older from selected households were interviewed with an overall response rate of 97%. Primary outcomes were hypertension and normal blood pressure defined by the widely used Seventh Report of the Joint National Committee (JNC7) and the American College of Cardiology/American Heart Association (ACC/AHA) 2017. Results The prevalence of hypertension was higher in Nepalese men than women. The likelihood of being hypertensive was significantly higher in the higher education group compared with the lowest or no education group for men (OR 1.89 95% CI: 1.36, 2.61) and for women (OR 1.20 95% CI: 0.79, 1.83). People in the richest group were more likely to be hypertensive compared with people in the poorest group for men (OR 1.66 95% CI: 1.26, 2.19) and for women (OR 1.60 95% CI: 1.20, 2.12). The associations between SES (education) and hypertension were partially modified by sex and fully modified by urbanity. BMI mediated these associations. Conclusions The higher SES was positively associated with the higher likelihood of having hypertension in Nepal according to both JNC7 and ACC/AHA 2017 guidelines. These associations were mediated by BMI, which may help to explain broader socioeconomic differentials in cardiovascular disease (CVD) and related risk factors, particularly in terms of education and wealth. Our study suggests that the mediating factor of BMI should be tackled to diminish the risk of CVD in people with higher SES in LMICs.