Currently, there is an increased interest from both scientists and consumers in the application of cannabis/hemp/phytocannabinoids in skin-related disorders. However, most previous investigations assessed the pharmacological properties of hemp extracts, cannabidiol (CBD), or tetrahydrocannabinol (THC), with very few studies focusing on minor phytocannabinoids from hemp. In this context, the current work explored the in vitro anti-melanoma, anti-melanogenic, and anti-tyrosinase effects of cannabidiol (CBD) and three minor phytocannabinoids, namely cannabigerol (CBG), cannabinol (CBN), and cannabichromene (CBC). Among the tested human malignant melanoma cells (A375, SH4, and G361), only A375 cells were highly susceptible to the 48 h treatment with the four phytocannabinoids (IC50 values between 12.02 and 25.13 μg/mL). When melanogenesis was induced in murine melanoma B16F10 cells by α-melanocyte stimulating hormone (αMSH), CBD, CBG, and CBN significantly decreased the extracellular (29.76–45.14% of αMSH+ cells) and intracellular (60.59–67.87% of αMSH+ cells) melanin content at 5 μg/mL. Lastly, CBN (50–200 μg/mL) inhibited both mushroom and murine tyrosinase, whereas CBG (50–200 μg/mL) and CBC (100–200 μg/mL) down-regulated only the mushroom tyrosinase activity; in contrast, CBD was practically inactive. The current data show that tyrosinase inhibition might not be responsible for reducing the melanin biosynthesis in α-MSH-treated B16F10 cells. By evaluating for the first time the preliminary anti-melanoma, anti-melanogenic, and anti-tyrosinase properties of CBN and CBC and confirming similar effects for CBD and CBG, this study can expand the utilization of CBD and, in particular, of minor phytocannabinoids to novel cosmeceutical products for skin care.