The worldwide increase in serious infections caused by multidrug-resistant (MDR) K. pneumoniae emphasizes the urgent need of new therapeutic strategies for the control of this pathogen. There is growing interest in the use of bacteriophages (or phages) to treat K. pneumoniae infections, and newly isolated phages are needed. Here, we report the isolation and physical/biological/molecular characterization of a novel lytic phage and its efficacy in the control of MDR K. pneumoniae. The phage vB_KpnS_Uniso31, referred to hereafter as phage Kpn31, was isolated from hospital wastewater using K. pneumoniae CCCD-K001 as the host. Phage Kpn31 presents a siphovirus-like morphotype and was classified as Demerecviridae; Sugarlandvirus based on its complete genome sequence. The 113,444 bp Kpn31 genome does not encode known toxins or antimicrobial resistance genes, nor does it encode depolymerases related sequences. Phage Kpn31 showed an eclipse time of 15 min and a burst size of 9.12 PFU/host cell, allowing us to conclude it replicates well in K. pneumoniae CCCD-K001 with a latency period of 30 min. Phage Kpn31 was shown to be effective against at least six MDR K. pneumoniae clinical isolates in in vitro antibacterial activity assays. Based on its features, phage Kpn31 has potential for controlling infections caused by MDR K. pneumoniae.