Background: Klebsiella pneumoniae is a nosocomial pathogen that causes severe infections in immunocompromised patients. The aim of the study was to conduct a microbiological and clinical analysis of K. pneumoniae infections in children with malignancies or undergoing hematopoietic cell transplantation in Poland. Methods: We conducted a retrospective, multicenter study including children and adolescents under 19 years old treated between 2012 and 2021. We analyzed patients’ characteristics, microbiological data, and the outcomes of antibiotic therapy. Results: A total of 9121 newly diagnosed children were treated for malignancy and 1697 pediatric patients underwent hematopoietic cell transplantation. K. pneumoniae infections were diagnosed in 527 patients. Their overall incidence was 4.86% in pediatric hematology and oncology patients and 4.95% in patients who underwent hematopoietic cell transplantation. The incidence of infection was higher in patients with acute leukemia than with solid tumors (7.8% vs. 4.1%; OR = 2.0; 95% CI = 1.6–2.4; p < 0.0001). The most frequent source of infection was in the urinary tract at 55.2%. More than 57% of K. pneumoniae strains were extended-spectrum β-lactamase-positive and almost 34% were multidrug-resistant. Infections with K. pneumoniae contributed to death in 3.22% of patients. Conclusions: K. pneumoniae is one of the most critical pathogens in children suffering from malignancies or undergoing hematopoietic cell transplantation. The incidence of multidrug-resistant K. pneumoniae strains is increasing and contributing to poor clinical outcome.