Nowadays, mastitis is one of the biggest problems in breeding dairy cattle. Treatment of this disease with conventional antibiotics is ineffective because many pathogens are resistant. Researchers have therefore been forced to look for new solutions, and metal nanoparticles (NPs) have been found to be the most appropriate agents. This study uses commercially available silver (AgNPs) and copper (CuNPs) nanoparticles and synthetized silver–copper nanoparticles (AgCuNPs) to evaluate the effect of these NPs on human and bovine mammary cells. The effect of AgNPs, CuNPs, and AgCuNPs on pathogen species commonly involved in udder inflammation (e.g., Staphylococcus aureus and Escherichia coli) was also established. The results show that commercially available NPs were of good quality and did not have a toxic effect on mammary gland tissue. AgNPs, CuNPs, and AgCuNPs also influenced or decreased the viability of pathogens. Therefore, the presented data suggest that metal NPs could be used in mastitis prevention and treatment in the future. However, the presented preliminary results require further in vivo analysis.