Antibiotic resistance poses an important threat to global public health and has become a challenge to modern medicine. The occurrence of antibiotic-resistant bacteria in a broad range of foods has led to a growing concern about the impact that food may have as a reservoir of antibiotic resistance genes. Considering Minas Frescal Cheese (MFC)—a typical Brazilian white soft cheese—and its economic and cultural values, in this study, medically relevant antimicrobial-resistance genetic markers (AR genes) were screened, and the occurrence of integrons were evaluated in manufactured MFC using culture-independent approaches. Through a fingerprinting analysis, the tested MFCs were brand-clustered, indicating reproducibility along the production chain. A common core of resistance markers in all brands evaluated and related antimicrobials such as β-lactams, tetracyclines, quinolones, and sulfonamide was detected. Several other markers, including efflux pumps and aminoglycosides-resistance were distributed among brands. Class 1 and 2 integrons were observed, respectively, in 77% and 97% of the samples. The presence of AR genes is of special interest due to their clinical relevance. Taken together, the data may suggest that the production chain of MFC might contribute to the spread of putative drug-resistant bacteria, which could greatly impact human health. Furthermore, detection of class 1 and class 2 integrons in MFC has led to discussions about resistance gene spread in this traditional cheese, providing evidence of potential horizontal transfer of AR genes to human gut microbiota.