Antimicrobial resistance is one of the major clinical concerns, making the discovery of new antimicrobial drugs desirable. Moringin (MOR), the major isothiocyanate produced from Moringa oleifera seeds, could represent an alternative therapeutic strategy to commonly used antibiotics. The aim of our study was to investigate the antimicrobial effect of MOR conjugated with α-cyclodextrin (MOR/α-CD), a complex with an improved solubility and stability in aqueous solutions. Our data demonstrated that MOR/α-CD was able to exert antimicrobial activity against the S. aureus reference strains (ATCC 25923, ATCC 6538, and ATCC BAA-977). Moreover, MOR/α-CD showed bacteriostatic effects (MIC = minimum inhibitory concentration = 0.5 mg/mL) and bactericidal properties (MBC = minimum bactericidal concentration = 1 mg/mL) against the overall assessed strains. In addition, MOR/α-CD showed bactericidal activity against the S. aureus strain ATCC BAA-977 after treatment with erythromycin (Ery), which induced clindamycin-resistance on the erm (A) gene. This evidence led us to assume that MOR/α-CD could be a promising antimicrobial agent against strains with the clindamycin-resistant phenotype (CC-resistant).