The rise of antibiotic-resistant Klebsiella pneumoniae, a leading nosocomial pathogen, prompts the need for alternative therapies. We have identified and characterized a novel depolymerase enzyme encoded by Klebsiella phage KP36 (depoKP36), from the Siphoviridae family. To gain insights into the catalytic and structural features of depoKP36, we have recombinantly produced this protein of 93.4 kDa and showed that it is able to hydrolyze a crude exopolysaccharide of a K. pneumoniae host. Using in vitro and in vivo assays, we found that depoKP36 was also effective against a native capsule of clinical K. pneumoniae strains, representing the K63 type, and significantly inhibited Klebsiella-induced mortality of Galleria mellonella larvae in a time-dependent manner. DepoKP36 did not affect the antibiotic susceptibility of Klebsiella strains. The activity of this enzyme was retained in a broad range of pH values (4.0–7.0) and temperatures (up to 45 °C). Consistently, the circular dichroism (CD) spectroscopy revealed a highly stability with melting transition temperature (Tm) = 65 °C. In contrast to other phage tailspike proteins, this enzyme was susceptible to sodium dodecyl sulfate (SDS) denaturation and proteolytic cleavage. The structural studies in solution showed a trimeric arrangement with a high β-sheet content. Our findings identify depoKP36 as a suitable candidate for the development of new treatments for K. pneumoniae infections.