Multidrug resistant (MDR) Klebsiella pneumoniae is a common cause of nosocomial infections worldwide. Recent years have seen an explosion of resistance to extended-spectrum β-lactamases (ESBLs) and emergence of carbapenem resistance. Here, we examine 198 invasive K. pneumoniae isolates collected from over a decade in Kilifi County Hospital (KCH) in Kenya. We observe a significant increase in MDR K. pneumoniae isolates, particularly to third generation cephalosporins conferred by ESBLs. Using whole-genome sequences, we describe the population structure and the distribution of antimicrobial resistance genes within it. More than half of the isolates examined in this study were ESBL-positive, encoding CTX-M-15, SHV-2, SHV-12 and SHV-27, and 79% were MDR conferring resistance to at least three antimicrobial classes. Although no isolates in our dataset were found to be resistant to carbapenems we did find a plasmid with the genetic architecture of a known New Delhi metallo-β-lactamase-1 (NDM)-carrying plasmid in 25 isolates. In the absence of carbapenem use in KCH and because of the instability of the NDM-1 gene in the plasmid, the NDM-1 gene has been lost in these isolates. Our data suggests that isolates that encode NDM-1 could be present in the population; should carbapenems be introduced as treatment in public hospitals in Kenya, resistance is likely to ensue rapidly.