Tyrosinases belong to the functional copper-containing proteins family, and their structure contains two copper atoms, in the active site, which are coordinated by three histidine residues. The biosynthesis of melanin in melanocytes has two stages depending on the actions of the natural substrates L-DOPA and L-tyrosine. The dysregulation of tyrosinase is involved in skin cancer initiation. In the present study, using molecular modeling tools, we analyzed the inhibition activity of tyrosinase activity using kojic acid (KA) derivatives designed from aromatic aldehydes and malononitrile. All derivatives showed conformational affinity to the enzyme active site, and a favorable distance to chelate the copper ion, which is essential for enzyme function. Molecular dynamics simulations revealed that the derivatives formed promising complexes, presenting stable conformations with deviations between 0.2 and 0.35 Å. In addition, the investigated KA derivatives showed favorable binding free energies. The most stable KA derivatives showed the following binding free energies: −17.65 kcal mol−1 (D6), −18.07 kcal mol−1 (D2), −18.13 (D5) kcal mol−1, and −10.31 kcal mol−1 (D4). Our results suggest that these derivatives could be potent competitive inhibitors of the natural substrates of L-DOPA (−12.84 kcal mol−1) and L-tyrosine (−9.04 kcal mol−1) in melanogenesis.