UV-A (315–400 nm) is a component of solar radiation, which impacts plant physiology. Consequently, the impact was investigated of UV-A supplementation on various aspects of kale cultivation in a plant factory with artificial lighting. Three UV-A intensity treatments (5, 10, or 15 W/m2) were applied to kale plants for 5 days before harvesting. The results revealed that 5 or 10 W/m2 UV-A supplementation provided significant advantages for kale growth. The fresh weight of the kale shoots increased by over 35–50% after UV-A exposure. In particular, the 10 W/m2 UV-A exposure significantly improved the photosynthetic rate, water-use efficiency, and quantum efficiency of photosystem II (Y(II)). In addition, the treatment with UV-A positively impacted changes in leaf spectral indices, resulting in decreases in the simple ratio index (SR), the normalized phaeophytinization index (NPQI), and the normalized difference red edge index (NDRE). Furthermore, the phytonutrients in kale (Vitamin C, soluble protein, and total phenolics) were enhanced using the 10 W/m2 UV-A treatment. One notable outcome was the consistent reduction in nitrate contents across all UV-A treatment intensities. Therefore, supplementing kale cultivation with UV-A radiation was a valuable strategy for enhancing kale yield and quality in plant factory production.