The transmission of zoonotic bacteria through consumption of raw milk is complicated by the dissemination of antimicrobial-resistant bacteria. The present study was conducted to detect the occurrence of antimicrobial-resistant bacteria (ESBL-/AmpC-producing Klebsiella spp.) in cow’s milk originating from healthy or infected (mastitis) cattle in India. In total, 450 milk samples were collected from apparently healthy cattle and cattle suffering from clinical or sub-clinical mastitis. Out of 455 Klebsiella spp., 67 (14.73%) isolates were found to be ESBL producers in the double-disc diffusion test. The occurrence of ESBL-producing Klebsiella spp. was significantly (p < 0.05) higher in milk samples collected from cattle suffering with mastitis than in healthy cattle. Among the ESBL-producing Klebsiella spp., 56 (83.6%) isolates were also detected that produced AmpC β-lactamases. All the ESBL and AmpC-producing Klebsiella spp. possessed blaCTX-M (100%) and blaAmpC (100%), respectively. The present study revealed a higher occurrence of class 1 integron in ESBL-producing Klebsiella spp. isolates. All ESBL-producing- Klebsiella spp. isolates were multi-drug resistant. The ciprofloxacin- and/or levofloxacin-resistant Klebsiella spp. isolates possessed the quinolone resistance gene (qnrS). The co-trimoxazole-resistant isolates possessed the sul1 and sul2 genes. Phylogenetic analysis of the studied isolates revealed that strains isolated from the same location had a clonal relationship. The study increases consumer awareness of the need to avoid raw milk consumption to prevent the spread of antimicrobial resistance in the community.