Generic medications are common solutions for reducing pharmaceutical costs. This study aimed to estimate the total cost of drugs prescribed in selected primary health care centers for managing hypertension and the potential savings from substituting generic drugs. One thousand patients with hypertension were randomly selected from the Primary Care Information System database from Al-Jahra governorate in Kuwait from January to December 2018. Generic antihypertensive drugs were substituted for branded ones, and cost savings were calculated by referring to the International Drug Price Indicator Guide. Mean age of 1,000 patients was 57.01 (SD = 11.82) years. Most (57.4%) patients were females, and 50.2% were Kuwaitis. The mean number of drugs per prescription was 1.78 (SD = 1.25; range: 1 to 9 drugs). The total number of drugs prescribed was 1,781, with a cost of KD 10,093 and mean of KD 10.09 (SD = 7.34). Only 71 generic drugs had been prescribed, making the generic prescription rate 4%. The total number of antihypertensive drugs prescribed was 1,206 (mean: 1.21; SD = 0.46), with a cost of KD 7,678.5 (mean = KD 7.68; SD = 4.06) and with ACEI as the most prescribed class at 32.19%. Eight hundred and ninety antihypertensive drugs were substituted at estimated savings of KD 5,675; that is, substituting reduced antihypertensive drug cost by 74%. Generic drug prescription appears to be low among primary care physicians in health care centers in Kuwait, but these centers could see substantial cost savings from substituting generic antihypertensive drugs for branded ones.