Hypertension is a major risk factor for dementia. Yet, the most suitable cognitive screening test for hypertensive patients has yet to be identified. This study investigated cognitive impairment in hypertensive older adults and compared the discriminative ability of the most widely used cognitive screening tests. The study involved hypertensive patients aged 65+ without prior diagnosis of cognitive impairment, from the Hypertension Clinic of Careggi Hospital, Florence, Italy. Mini Mental State Examination (MMSE), Montreal Cognitive Assessment (MoCA), MiniCog and Clock Drawing Test (CDT) were administered, using a comprehensive neuropsychological assessment as gold standard. The ROC curve analysis and the paired chi-square test were used to compare the discriminative ability, sensitivity and specificity for cognitive impairment of the different screening instruments. Cognitive impairment was diagnosed in 37% of 94 participants (mean age 76, 55% female), mainly involving attention and executive functions. The MoCA (AUC = 0.746), the MMSE (AUC = 0.689) and the MiniCog (AUC = 0.684) showed similar ability in detecting cognitive impairment, while the CDT had a poorer discriminative capacity (AUC = 0.535). The sensitivity of MoCA (80%) and of MMSE/MiniCog combination (74%) was higher in comparison with MiniCog alone (49%, p = 0.007 and 0.004, respectively), while MiniCog achieved the highest specificity (88%, p < 0.001 vs all). Cognitive impairment was detected in more than one-third of hypertensive older adults without prior diagnosis of dementia. MoCA, MMSE and MiniCog showed similar discriminative ability for cognitive impairment, with MoCa and MMSE showing greater sensitivity and MiniCog the highest specificity.