Background: Klebsiella is an important causative organism of neonatal sepsis (NS), particularly in developing countries. This study aimed to analyze the demographic and clinical laboratory features of a fatal outbreak of Klebsiella spp. that occurred in a neonatal intensive care unit (NICU), identify the source of the infections, and propose infection control measures to prevent future occurrences. Methods: We performed a retrospective analysis of the medical records and investigative reports of sepsis cases caused by Klebsiella pneumoniae admitted to the neonatal units of a tertiary care teaching hospital in western India from May to August 2022. Results: Among the 26 neonates with Klebsiella sepsis, those born at <28 weeks and 28–32 weeks of gestation were the most affected group. The mortality rate was high (n = 21, 80%). The C-reactive protein (CRP) level was used to assess the severity and prognosis of the infection. The platelet count (PLT) decreased significantly from day 1 to 15 (p < 0.001) as the condition worsened. Elevated CRP levels (>100 mg/L) were also observed on the 5th day of admission (p < 0.001). We found unsatisfactory hand hygiene practices, and K. pneumoniae grew on surface swab sampling of wash basins and overhead water tanks. Thorough decontamination of the source of infection and strengthening of infection control practices was performed. Conclusion: Carbapenem-resistant Klebsiella strains led to substantial morbidity and mortality during an outbreak in neonates.