Anthropometric indicators of general and abdominal obesity can predict cardiovascular disease outcomes. Their performance in predicting hypertension (HTN) varies across populations. We aimed to analyze the relationship of body mass index (BMI), waist circumference (WC), waist-to-height ratio (WHtR) and conicity index (CI) with HTN, to examine their predictive performance and to determine their optimal cut-offs in a nationally representative sample of Albanians aged 15–59 years (n = 20,635). Logistic regression models were fitted and sex-specific receiver-operating characteristic (ROC) curves were constructed. The indicators were positively associated with HTN. Sex modified the relationships, as associations appeared significantly stronger among females than males in the highest categories of the indicators. The area under ROC curves (AUCs) for BMI were 0.729 (95% confidence interval (CI): 0.720–0.738) among females and 0.648 (95% CI: 0.633–0.663) among males, and AUCs for WHtR were 0.725 (95% CI: 0.716–0.734) among females and 0.637 (95% CI: 0.622–0.652) among males. However, the AUCs for BMI and WHtR did not differ significantly among females (p = 0.279) and males (p = 0.227). BMI outperformed WC and CI in both sexes. The optimal BMI cut-offs were 27.0 kg/m2 among females and 25.6 kg/m2 among males, and that for WHtR were 0.53 among females and 0.54 among males. BMI and WHtR demonstrated similar discriminatory power, and the identified cut-offs may inform initiatives for structured HTN screening in Albania.