Klebsiella oxytoca is an emerging opportunistic pathogen capable of causing bovine mastitis and neonatal colonization. This study provides a comprehensive molecular and phenotypic characterization of K. oxytoca across dairy supply nodes and pediatric host matrices while evaluating a probiotic-based bio-intervention strategy. K. oxytoca was isolated from 27.9% (39/140) of examined samples across dairy supply nodes and infant stool in Egypt, with equal peak prevalence in clinical mastitic milk (40.0%, 8/20) and infant fecal specimens (40.0%, 8/20). High rates of multidrug resistance (MDR; 66.7%, 26/39) were observed, with all isolates (100%) confirmed as extended-spectrum β-lactamase (ESBL) producers. Colistin (CT) and azithromycin resistance reached 46.2% (18/39) overall, peaking in commercial milk (69.2% for CT). Molecular screening revealed high frequencies of the mobile colistin resistance gene mcr-1 (41.0%, 16/39) and the ESBL determinant blaCTX-M (66.7%, 26/39), alongside fimbrial adhesion (mrkA, 76.9%) and iron acquisition (kfuBC, 82.1%) loci. All isolates (100%) exhibited strong biofilm-forming capacity (mean OD₅₇₀ = 0.63 ± 0.016), while toxin-antitoxin (TA) modules (symE, ccdB, relE) correlated positively with MDR profiles (p = 0.024). Bacterial virulence gene burden showed strong statistical associations with host tissue damage and inflammatory markers, including elevated milk lactate dehydrogenase (LDH; r = 0.918), haptoglobin (r = 0.954), and neonatal fecal calprotectin (FC; 83.34 ± 21.13 μg/g vs. 22.4 ± 2.0 μg/g in controls, p = 0.02). Crucially, milk-based cell-free metabolic supernatant (CFS) from Lactobacillus acidophilus demonstrated superior antagonistic activity compared to broth-based CFS (inhibition zones up to 40 mm vs. 12 mm against CT-resistant isolates). In silico molecular docking predicted strong binding affinities of putative L. acidophilus bioactive peptides (Acidocin 8912 score: −108.07 kcal/mol; Acidocin B score: 80.63 kcal/mol) to K. oxytoca outer membrane porin CymA and transport targets. These findings highlight the co-occurrence of resilient K. oxytoca lineages across food and pediatric matrices and demonstrate the therapeutic potential of probiotic-derived CFS as a non-antibiotic control strategy within a One Health framework.