This study aimed to produce, analyze, and evaluate the consumer acceptance of caffeine-enriched (15, 30, 60, and 90 mg/100 mL) grape must, which does not contain any added sweeteners or preservatives, to meet today’s popular health-conscious consumer trends. Regarding acid composition, the musts contained malic acid (426.96–491.58 mg/100 mL) and succinic acid (74.53–84.79 mg/100 mL). Musts are regarded as water-soluble sugars, containing only glucose (6158.81–9417.09 mg/100 mL) and fructose (6798.37–10,482.53 mg/100 mL), which are typical in fruits. The must’s TPC and TAC contents were determined to be between 11.42 and 14.14 mg GAE/100 mL, and 8.14 and 11.80 mg AAE/100 mL, respectively. During the analysis of caffeine content, recovery values of 93.89–96.98% were determined. The must samples containing 60 and 90 mg/100 mL caffeine had too intense a bitter flavor; thus, the enjoyment value of the products was reduced based on consumer feedback. The must containing 15 mg/100 mL of caffeine had the most favorable organoleptic properties.