Yarrowia lipolytica yeast are able to produce kynurenic acid—a very valuable compound acting as a neuroprotective and antioxidant agent in humans. The recent data proved the existence of the kynurenine biosynthesis pathway in this yeast cells. Due to this fact, the aim of this work was to enhance kynurenic acid production using crude glycerol and soybean molasses as cheap and renewable carbon and nitrogen sources. The obtained results showed that Y. lipolytica GUT1 mutants are able to produce kynurenic acid in higher concentrations (from 4.5 mg dm−3 to 14.1 mg dm−3) than the parental strain (3.6 mg dm−3) in the supernatant in a medium with crude glycerol. Moreover, the addition of soybean molasses increased kynurenic acid production by using wild type and transformant strains. The A-101.1.31 GUT1/1 mutant strain produced 17.7 mg dm−3 of kynurenic acid in the supernatant during 150 h of the process and 576.7 mg kg−1 of kynurenic acid in dry yeast biomass. The presented work proves the great potential of microbial kynurenic acid production using waste feedstock. Yeast biomass obtained in this work is rich in protein, with a low content of lipid, and can be a healthy ingredient of animal and human diet.