The ASTRI Mini-Array is an array of nine small-sized (4-m diameter) and large field of view ($\sim$10$^\circ$) imaging atmospheric Cherenkov telescopes under deployment at the {\itshape Observatorio del Teide} (Tenerife, Spain). The system is sensitive to $\gamma$-ray radiation in the energy range $1 \div 200$ TeV. The telescopes are characterized by a dual-mirror optical system and equipped with silicon photo-multiplier cameras. These sensors can be operated under relatively high levels of night-sky background, thus allowing us to extend the duty cycle of Cherenkov observations beyond the "dark" regime alone. In order to assess the performance of the system with different night-sky brightness conditions, a study of the intensity and spectral shape of the illumination at the Teide Observatory site as a function of the array pointing direction and of the lunar phase has been carried out. Then, dedicated Monte Carlo simulations have been generated with a set of increasing brightness levels and subsequently reduced with A-SciSoft (ASTRI Scientific Software), the official scientific software package of the ASTRI Project. In this contribution, we present the performance of the ASTRI Mini-Array achieved with the aforementioned MC simulations, discussing the implications of our finding on the duty cycle of the system and its scientific potentialities.