Background/Objectives: A well-established association exists between the development of hypertension and sleep quality. The connection between self-reported sleep quality and the onset of hypertension is particularly significant in populations with metabolic deterioration, such as in Mexico. Methods: The Tlalpan 2020 Cohort was analyzed to explore this association. Clinical and anthropometric characteristics, along with the Medical Outcomes Study Sleep Scale (MOS-SS), were compared between participants who developed hypertension and those who did not over a follow-up period of 30.8 months. The potential role of poor sleep quality in the development of hypertension was assessed. Results: Among 1520 participants, 12% developed hypertension. These individuals had higher anthropometric and laboratory values and reported poorer sleep quality. An elevated sleep problems index was associated with a 50% higher relative risk of developing hypertension (OR: 1.5; 95% CI: 1.087 to 2.069). Additionally, self-reported snoring was associated with hypertension onset (36.3 vs. 43.3; p = 0.019). Conclusions: Poor sleep quality and respiratory disturbances during sleep increase the risk of developing hypertension. Furthermore, hypertension was associated with snoring, highlighting the importance of early interventions to improve sleep quality.