This study aimed to analyze the frequency of blaTEM, blaSHV, and blaCTX-M encoding genes in ESBL-producing Klebsiella pneumoniae isolates from various clinical specimens obtained from the Ukrainian Children`s Cardiac Center in Kyiv, Ukraine (2018–2021). Antibiotic susceptibility was performed by the standardized Kirby–Bauer disk diffusion method and phenotypic double-disk synergy tests were used for screening of ESBL production. Detection of bla genes was performed by multiplex gel-based PCR. Among the 75 samples investigated, 40 were from male patients and 35 were from females. Most of the patients were in the pediatric (n = 34) and newborns (n = 22) groups. Most K. pneumoniae isolates were cultured from blood (n = 22), sputum (n = 21), and the respiratory tract (n = 18). The prevalence of ESBL-producing K. pneumoniae, among antibiotic resistant K. pneumoniae was 75.6% in 2018, 84.7% in 2019, 89.3% in 2020, and 88.2% in 2021. In total, 75 ESBL-producing K. pneumoniae were 100.0% resistant to cefuroxime and ceftriaxone and showed high resistance to other antibiotics, including carbapenems. In total, 69 of the 75 isolates were PCR positive for one or more of these three bla genes. The study shows a predominance of blaCTX-M in the investigated strains. The prevalence of blaCTX-M, blaTEM, and blaSHV genes among the isolates was 84.1%, 53.6%, and 52.9%, respectively. More than half (63.8%) of the ESBL-producing K. pneumoniae isolates were positive for at least two ESBL genes. In addition, 26.1% of the isolates harbored all three of these bla genes. This study presents the prevalence of three important bla genes in ESBLs-producing K. pneumoniae and reveals a dramatic increase in the resistance of K. pneumoniae to the third-generation of cephalosporins in recent years. This suggests a need for more epidemiological studies, and a need to strengthen infection prevention and control measures in Ukraine.