Background: Hypertension imposes a significant public health burden. An increased awareness of hypertension complications within a population can positively impact patient care and prevent complications. This study seeks to assess the awareness of hypertension complications among the population of Bisha in Saudi Arabia in 2020. Methods: A cross-sectional study was conducted in 2020. A validated self-administered online-based questionnaire was sent to a sample of the adult population of Bisha to measure their awareness of hypertension complications. Results: Almost three-quarters of the population (72.2%) were aware of hypertension complications. The awareness level was significantly higher among male participants (p < 0.001), those aged 31–40 years, those who were married, those working as police officers or in civilian jobs, those living in urban areas (p = 0.04), those with a university-level education (p = 0.03), those with a medium family income (SAR 5000–14,999) (p = 0.001), and those with a history of hospitalization because of causes other than hypertension (p = 0.05). Marital status was independently predictive of awareness (B = 0.851, Wald test = 12.179, p = 0.000) among the respondents. Conclusion: The study concludes that the awareness of hypertension complications among the Bisha population in Saudi Arabia was deemed acceptable. Factors such as marital status, age, gender, a family history of hypertension, the duration of hypertension, and medication adherence positively influenced this awareness and served as predictors of hypertensive awareness. The findings highlight the importance of health authorities in ensuring the widespread awareness of hypertension complications, particularly among hypertensive individuals.