Aim: This study investigated the spectrum of bacteria infecting the ulcers of individuals with diabetes at the Korle Bu Teaching Hospital in Accra, Ghana, focusing on Staphylococcus aureus (S. aureus) and methicillin-resistant S. aureus (MRSA), with respect to their prevalence, factors predisposing to their infection of the ulcers, and antimicrobial resistance patterns. Methodology: This cross-sectional study was conducted at The Ulcer Clinic, Department of Surgery, Korle Bu Teaching Hospital, involving 100 diabetic foot ulcer patients. The ulcer of each study participant was swabbed and cultured bacteriologically, following standard procedures. Antimicrobial susceptibility testing was done for all S. aureus isolated, using the Kirby-Bauer method. Results: In total, 96% of the participants had their ulcers infected—32.3% (n = 31) of these had their ulcers infected with one bacterium, 47.9% (n = 46) with two bacteria, 18.8% (n = 18) with three bacteria, and 1.0% (n = 1) with four bacteria. The prevalence of S. aureus and MRSA were 19% and 6%, respectively. The distribution of the other bacteria was as follows: coagulase-negative Staphylococci (CoNS) (54%), Escherichia coli (24%), Pseudomonas spp. (19%), Citrobacter koseri and Morganella morgana (12% each), Klebsiella oxytoca (11%), Proteus vulgaris (8%), Enterococcus spp. (6%), Klebsiella pneumoniae (5%), Proteus mirabilis and Enterobacter spp. (4%), Klebsiella spp. (2%), and Streptococcus spp. (1%). The resistance rates of S. aureus decreased across penicillin (100%, n = 19), tetracycline (47.4%, n = 9), cotrimoxazole (42.1%, n = 8), cefoxitin (31.6%, n = 6), erythromycin and clindamycin (26.3% each, n = 5), norfloxacin and gentamicin (15.8% each, n = 3), rifampicin (10.5%, n = 2), linezolid (5.3%, n = 1), and fusidic acid (0.0%, n = 0). The proportion of multidrug resistance was 47.4% (n = 9). Except for foot ulcer infection with coagulase-negative Staphylococci, which was protective of S. aureus infection of the ulcers (OR = 0.029, p = 0.001, 95% CI = 0.004–0.231), no predictor of S. aureus, MRSA, or polymicrobial ulcer infection was identified. Conclusions: The prevalence of S. aureus and MRSA infection of the diabetic foot ulcers were high, but lower than those of the predominant infector, coagulase-negative Staphylococci and the next highest infecting agent, E. coli. Diabetic foot ulcers’ infection with coagulase-negative Staphylococci protected against their infection with S. aureus. The prevalence of multidrug resistance was high, highlighting the need to further intensify antimicrobial stewardship programmes.