Background Antimicrobial resistance among pathogens of public health importance is an emerging problem in sub-Saharan Africa. Unfortunately, published information on the burden and patterns of antimicrobial resistance (AMR) in this region is sparse. There is evidence that the burden and patterns of AMR vary by geography and facility. Knowledge of local epidemiology of AMR is thus important for guiding clinical decisions and mitigation strategies. Therefore, the objective of this study was to determine the burden and predictors of AMR and multidrug resistance (MDR) among bacterial pathogens isolated from specimens submitted to the diagnostic laboratory of a hospital in Nairobi, Kenya. Methods This retrospective study used laboratory records of 1,217 clinical specimens submitted for bacterial culture and sensitivity testing at the diagnostic laboratory of The Karen Hospital in Nairobi, Kenya between 2012 and 2016. Records from specimens positive for Enterobacteriaceae, Staphylococcus aureus, or Pseudomonas spp. isolates were included for analysis. Firth logistic models, which minimize small sample bias, were used to investigate determinants of AMR and MDR of the isolates. Results A total of 222 specimens had bacterial growth. Most Enterobacteriaceae isolates were resistant to commonly used drugs such as penicillin/β-lactamase inhibitor combinations (91.2%) and folate pathway inhibitors (83.7%). Resistance to extended-spectrum cephalosporins was also high (52.9%). Levels of AMR and MDR for Enterobacteriaceae were 88.5% and 51%, respectively. Among S. aureus isolates, 57.1% were AMR, while 16.7% were MDR. As many as 42.1% of the Pseudomonas spp. isolates were aminoglycoside-resistant and 15% were fluoroquinolone-resistant, but none exhibited resistance to antipseudomonal carbapenems. Half of Pseudomonas spp. isolates were AMR but none were MDR. Significant predictors of MDR among Enterobacteriaceae were organism species (p = 0.002) and patient gender (p = 0.024). Conclusions The high levels of extended-spectrum cephalosporin resistance and MDR among Enterobacteriaceae isolates are concerning. However, the relatively low levels of MDR S. aureus, and an absence of carbapenem resistance among Pseudomonas isolates, suggests that last-line drugs are still effective against S. aureus and Pseudomonas infections. These findings are relevant for guiding evidence-based treatment decisions as well as surveillance efforts and directions for future research, and contribute to the sparse literature on AMR in sub-Saharan Africa.