Silver nanoparticles (AgNPs) were synthesized using aqueous honey solutions with a concentration of 2%, 10%, and 20%—AgNPs-H2, AgNPs-H10, and AgNPs-H20. The reaction was conducted at 35 °C and 70 °C. Additionally, nanoparticles obtained with the citrate method (AgNPs-C), while amphotericin B (AmB) and fluconazole were used as controls. The presence and physicochemical properties of AgNPs was affirmed by analyzing the sample with ultraviolet–visible (UV–Vis) and fluorescence spectroscopy, scanning electron microscopy (SEM), and dynamic light scattering (DLS). The 20% honey solution caused an inhibition of the synthesis of nanoparticles at 35 °C. The antifungal activity of the AgNPs was evaluated using opportunistic human fungal pathogens Candida albicans and Candida parapsilosis. The antifungal effect was determined by the minimum inhibitory concentration (MIC) and disc diffusion assay. The highest activity in the MIC tests was observed in the AgNPs-H2 variant. AgNPs-H10 and AgNPs-H20 showed no activity or even stimulated fungal growth. The results of the Kirby–Bauer disc diffusion susceptibility test for C. parapsilosis strains indicated stronger antifungal activity of AgNPs-H than fluconazole. The study demonstrated that the antifungal activity of AgNPs is closely related to the concentration of honey used for the synthesis thereof.