Staphylococcus aureus is a major foodborne pathogen. The ability of S. aureus to produce biofilm is a significant virulence factor, triggering its persistence in hostile environments. In this study, we screened a total of 420 different food samples and human hand swabs to detect S. aureus and to determine their biofilm formation ability. Samples analyzed were meat, milk, eggs, fish, fast foods, and hand swabs. S. aureus were detected by culturing, staining, biochemical, and PCR. Biofilm formation ability was determined by Congo Red Agar (CRA) plate and Crystal Violet Microtiter Plate (CVMP) tests. The icaA, icaB, icaC, icaD, and bap genes involved in the synthesis of biofilm-forming intracellular adhesion compounds were detected by PCR. About 23.81% (100/420; 95% CI: 14.17–29.98%) of the samples harbored S. aureus, as revealed by detection of the nuc gene. The CRA plate test revealed 20% of S. aureus isolates as strong biofilm producers and 69% and 11% as intermediate and non-biofilm producers, respectively. By the CVMP staining method, 20%, 77%, and 3% of the isolates were found to be strong, intermediate, and non-biofilm producers. Furthermore, 21% of S. aureus isolates carried at least one biofilm-forming gene, where icaA, icaB, icaC, icaD, and bap genes were detected in 15%, 20%, 7%, 20%, and 10% of the S. aureus isolates, respectively. Bivariate analysis showed highly significant correlations (p < 0.001) between any of the two adhesion genes of S. aureus isolates. To the best of our knowledge, this is the first study in Bangladesh describing the detection of biofilm-forming S. aureus from foods and hand swabs using molecular-based evidence. Our findings suggest that food samples should be deemed a potential reservoir of biofilm-forming S. aureus, which indicates a potential public health significance.