Enrofloxacin has a poor palatability and causes strong gastric irritation; the oral formulation of enrofloxacin is unavailable, which limits the treatment of Escherichia coli (E. coli) infections via oral administration. To overcome the difficulty in treating intestinal E. coli infections, an oral intelligent-responsive chitosan-oligosaccharide (COS)–sodium alginate (SA) composite core-shell nanogel loaded with enrofloxacin was explored. The formulation screening, characteristics, pH-responsive performance in gastric juice and the intestinal tract, antibacterial effects, therapeutic effects, and biosafety level of the enrofloxacin composite nanogels were investigated. The optimized concentrations of COS, SA, CaCl2, and enrofloxacin were 8, 8, 0.2, and 5 mg/mL, respectively. The encapsulation efficiency, size, loading capacity, zeta potential, and polydispersity index of the optimized formulation were 72.4 ± 0.8%, 143.5 ± 2.6 nm, 26.6 ± 0.5%, −37.5 ± 1.5 mV, and 0.12 ± 0.07, respectively. Scanning electron microscopy images revealed that enrofloxacin-loaded nanogels were incorporated into the nano-sized cross-linked networks. Fourier transform infrared spectroscopy showed that the nanogels were prepared by the electrostatic interaction of the differently charged groups (positive amino groups (-NH3+) of COS and the negative phenolic hydroxyl groups (-COO−) of SA). In vitro, pH-responsive release performances revealed effective pH-responsive performances, which can help facilitate targeted “on-demand” release at the target site and ensure that the enrofloxacin has an ideal stability in the stomach and a responsive release in the intestinal tract. The antibacterial activity study demonstrated that more effective bactericidal activity against E. coli could have a better treatment effect than the enrofloxacin solution. Furthermore, the enrofloxacin composite nanogels had great biocompatibility. Thus, the enrofloxacin composite core-shell nanogels might be an oral intelligent-responsive preparation to overcome the difficulty in treating intestinal bacterial infections.