Antimicrobial resistance (AMR) poses a significant global health challenge affecting food safety and development. Residues of antibiotics in food from animal sources, particularly milk, contribute to the development and spread of AMR, alter intestinal microbiota, and potentially lead to allergies, serious health conditions, and environmental and technological problems within the dairy industry. Therefore, this study investigated the residue levels of veterinary drugs from β-lactam antibiotics and tetracyclines in milk and milk products and assessed human health risks. Two hundred milk and milk product samples (pasteurized milk, sterile milk, soft white cheese, and processed cheese, 50 each) were collected from different hospitals in the State of Kuwait and screened for antibiotic residues using a microbial inhibition assay (Delvotest SP-NT) and high-performance liquid chromatography (HPLC). Delvotest SP-NT and HPLC analyses showed that 30, 28, 26, and 24% of the pasteurized milk, sterilized milk, white soft cheese, and processed cheese samples tested positive for antibiotic residues. Forty-eight milk and cheese samples were confirmed as positive by both methods, and six samples initially found to be negative by Delvotest SP-NT were confirmed as positive by HPLC. Multi-antibiotic residues were detected in five samples by using HPLC. The kappa coefficient (0.921; p < 0.0001) revealed complete concordance between the HPLC and Delvotest SP-NT results. Ampicillin was the most abundant residue in the positive samples (31.48%), ranging from 2.44 to 3.89 μg/L, with an overall mean concentration of 3.492 ± 0.094 μg/L, followed by tetracycline and oxytetracycline (27.78% each), ranging from 54.13 to 220.3 μg/L and from 41.55 to 160.7 μg/L, with mean concentrations of 129.477 ± 14.22 and 91.86 ± 9.92 μg/L, respectively. The amoxicillin levels in the samples (12/54; 22.22%) ranged from 3.11 to 5.5 μg/L, with an overall mean concentration of 3.685 ± 0.186 μg/L. The maximum concentrations of ampicillin, amoxicillin, and tetracycline were detected in processed cheese with mean concentrations of 3.89 ± 0.28 µg/L, 3.95 ± 0.15 µg/L, and 170.3 ± 0.27 µg/L, respectively. Pasteurized milk contained the maximum concentrations of oxytetracycline, with a mean concentration of 120.45 ± 0.25 µg/L. The tetracycline residues exceeded the standard maximum residue limits (MRLs; 100 µg/L) in 6% of both pasteurized and sterilized milk samples, and in 4% of processed cheese. Additionally, the oxytetracycline levels in pasteurized milk (6%) and amoxicillin levels in processed cheese (2%) were higher than the permitted MRLs (100 µg/L and 4 µg/L, respectively). Furthermore, the antibiotic residues detected in 12.5% (25/200) of the samples were close to standard permissible MRL limits for ampicillin (5%), amoxicillin and oxytetracycline (3% each), and tetracycline (1.5%). Hazard quotients, which compare the standard acceptable daily intake (ADI) to the estimated daily exposure (EDI), indicated that the overall risk associated with antibiotic residues in these dairy products is low. The EDI was lower than the ADI for the tested antibiotics, indicating an elevated safety margin. While the overall hazard quotients are low, the potential for the development of antibiotic resistance due to long-term exposure to low levels of antibiotics should be considered. Hence, strict regulations and enforcement are necessary to prevent excessive residue levels and to promote responsible antibiotic use in dairy production. Regular monitoring of antibiotic residues in dairy products is essential for ensuring consumer safety.