Background and Objectives: We aimed to explore the association between cognitive performance and markers of hypertension-mediated organ damage (HMOD) in young adults with hypertension. Materials and Methods: A group of adults aged 16 to 45 years with primary arterial hypertension completed a battery of paper-pencil as well as computer-based neuropsychological tests across all major cognitive domains. They also underwent office and ambulatory 24 h blood pressure, intima-media thickness measurements, heart ultrasound, and laboratory analysis of their lipid profile, blood uric acid concentration, and urine albumin-creatinine ratio. Associations between cognitive test results and markers of HMOD were explored through correlation analysis and age-, sex-, and body mass index-adjusted linear regression modeling. Results: Seventy-six individuals (62, 81.6% male) aged 36.5 years (interquartile range 18.4 to 42.0 years) were enrolled. After adjusting for age, sex, and body mass index in linear regression models, worse categorical fluency was associated with higher left ventricular mass (βst = -0.264, p = 0.043) and worse performance in a task of sustained attention-with higher left ventricular mass index (βst = -0. 304, p = 0.016). Worse phonemic fluency was related to higher pulse pressure (βst = -0.241, p = 0.049) in the respective model. Better strategy use in the task of spatial working memory was linked to higher daytime mean diastolic blood pressure (βst = -0.343 p = 0.017). Conclusions: Performance among young adults with hypertension across selected cognitive domains was inversely associated with pulse pressure, markers of left ventricular damage, and directly associated with daytime diastolic blood pressure. Our study suggests that the previously reported relationship between cognitive and cardiovascular markers in hypertension exists earlier than in middle or late adulthood.