ASTRI-Horn is the prototype of the nine telescopes that form the ASTRI Mini-Array, under construction at the Teide Observatory in Tenerife (Spain), devoted to observe the sky in the 1–200 TeV energy band. It adopts an innovative optical design based on a dual-mirror Schwarzschild-Couder configuration, and the camera, composed by a matrix of monolithic multipixel silicon photomultipliers (SiPMs) is managed by ad-hoc tailored front-end electronics based on a peak-detector operation mode. During the Crab Nebula campaign in 2018–2019, ASTRI-Horn was affected by gain variations induced by high levels of night sky background. This paper reports the work performed to detect and quantify the effects of these gain variations in shower images. The analysis requested the use of simultaneous observations of the night sky background flux in the wavelength band 300–650 nm performed with the auxiliary instrument UVscope, a calibrated multi-anode photomultiplier working in single counting mode. As results, a maximum gain reduction of 15% was observed, in agreement with the value previously computed from the variance of the night sky background level in each image. This ASTRI-Horn gain reduction was caused by current limitation of the voltage supply. The analysis presented in this paper provides a method to evaluate possible variations in the nominal response of SiPMs when scientific observations are performed in the presence of high night sky background as in moon conditions.