Simple Summary As the aging population is rapidly increasing worldwide, consumer interest in age-friendly foods and healthy foods is increasing. Recently, as the nutritional value of black goat meat has been proven, the consumption of black goats has increased. However, the best age of slaughter has not been established for black goats, and studies on meat characteristics according to the age of slaughter are also insufficient. Therefore, in this study, the physicochemical properties of black goat meat according to the slaughter age (3, 6, 9, 12, 24, and 36 months of age) were investigated. As the age of the black goats increased, the shear force, redness, and yellowness increased, and the brightness decreased. In addition, the results for water holding capacity, cooking yield, mineral content, and fatty acid composition, showed that it is appropriate to slaughter black goats after 12 months of age. This study was conducted to analyze the physicochemical properties of black goat meat according to the slaughter age (3, 6, 9, 12, 24, 36 months). The moisture content tended to decrease, whereas the fat content, pH, and free amino acid composition tended to increase with increasing slaughter age. The collagen content increased significantly with the increasing slaughter age (p < 0.05). The cooking yield showed a tendency to increase up to 12 months of age, and there was no significant difference after 12 months of age. In all mineral contents, the sample for 12 months of age showed higher values than the others. Considering fatty acid composition, the saturated fatty acid content of the 12-month sample had a lower value than the other samples. However, the unsaturated fatty acid of the 12-month sample had higher values than the other samples. Therefore, the best slaughter age for black goats occurs at 12 months of age when nutrition is excellent.