In agro-industrial processes, microorganisms that are not pathogenic and that generate molecules are generally recognized as safe (GRAS). The Aspergillus niger fungus has different industrial applications, being used to produce citric acid and 166 other secondary metabolites. The objective of this research was to optimize a culture medium to induce the production of kojic acid (KA) by the Aspergillus niger M4 strain in a liquid fermentation process. Four fermentative kinetics were developed in flasks, using different levels of yeast extract in (1) 0.05 g/L, (2) 0.10 g/L, (3) 2.5 g/L, and (4) 2.5 g/L + Zinc sulfate. The culture medium conditions influenced the formation and speed of biomass and the synthesis and yield of KA. The optimum production points were from 72 h and 96 h with 0.552 g/L and 0.510 g/L of KA using 2.5 g/L of yeast extract and with a pH of 5.5. The Aspergillus niger M4 strain had the ability to produce kojic acid, which was induced by the concentration of the nitrogen source.