Bovine mastitis is a common bovine disease, frequently affecting whole herds of cattle. It is often caused by resistant microbes that can create a biofilm structure. The rapidly developing scientific discipline known as nanobiotechnology may help treat this illness, thanks to the extraordinary properties of nanoparticles. The aim of the study was to investigate the inhibition of biofilms created by mastitis pathogens after treatment with silver and copper nanoparticles, both individually and in combination. We defined the physicochemical properties and minimal inhibitory concentration of the nanoparticles and observed their interaction with the cell membrane, as well as the extent of biofilm reduction. The results show that the silver–copper complex was the most active of all nanomaterials tested (biofilm was reduced by nearly 100% at a concentration of 200 ppm for each microorganism species tested). However, silver nanoparticles were also effective individually (biofilm was also reduced by nearly 100% at a concentration of 200 ppm, but at concentrations of 50 and 100 ppm, the extent of reduction was lower than for the complex). Nanoparticles can be used in new alternative therapies to treat bovine mastitis.