Background: Tyrosinase is a copper-dependent oxyreductase capable of catalyzing the oxidation of mono- and diphenols. Its activity is crucial in the biosynthetic pathway of melanin, the pigment responsible for the pigmentation of mammalian skin and fur, and protecting their skin from harmful UV radiation. Overproduction of this pigment leads to numerous pathological conditions, including the most severe form of skin cancer—malignant melanoma. Furthermore, tyrosinase produced in plant tissues leads to the browning of damaged vegetables and fruits. Therefore, the search for compounds that effectively and efficiently control tyrosinase activity is desirable for both pharmaceutical and food applications. Methods: A group of six boronate derivatives of thiosemicarbazones was synthesized, and their inhibitory properties against tyrosinase were determined. Furthermore, their ability to inhibit melanogenesis and proliferation in SK-MEL-3 and Hs294T cells was investigated. Docking simulations were performed to determine the nature of the inhibitor–protein interactions. Results: The tested inhibitors exhibited half-maximal inhibitory concentrations (IC₅₀) in the micromolar range. The best inhibitor, compound 6, had an IC₅₀ of 1.4 µM. The tested compounds exhibited poor selectivity for cell lines capable of high and low tyrosinase overexpression, with inhibitor 4 proving to be the most selective compound among those tested. Molecular modeling results indicate that the compounds with the highest activity against tyrosinase interact with the active cavity and the copper ions present within it via a boron moiety substituted on the aromatic ring of the thiosemicarbazones. Cell-based experiments indicated limited antiproliferative effects up to 100 µM across the tested lines. The compounds demonstrated weak antiproliferative effects in SK-MEL-3 and Hs-294T up to 100 µM. Conclusions: Our results show that the introduction of a boronic acid moiety is an alternative to carboxylic acid derivatives, improving the inhibitory activity of boron analogs (by fourfold) against fungal tyrosinase.