Beta-lactamase (β-lactamase)-producing Gram-negative bacteria (GNB) are of public health concern due to their resistance to routine antimicrobials. We investigated the antimicrobial resistance and occurrence of carbapenemases, extended-spectrum β-lactamases (ESBLs) and AmpCs among GNB from clinical sources. GNB were identified using matrix-assisted laser desorption/ionization time of flight–mass spectrometry (MALDITOF-MS). Antimicrobial susceptibility testing was performed via Kirby–Bauer disk diffusion and a microscan autoSCAN system. β-lactamase genes were determined via multiplex polymerase chain reactions. Of the 181 archived GNB analyzed, Escherichia coli and Klebsiella pneumoniae constituted 46% (n = 83) and 17% (n = 30), respectively. Resistance to ampicillin (51%), third-generation cephalosporins (21%), and ertapenem (21%) was observed among the isolates, with 44% being multi-drug resistant (MDR). β-lactamase genes such as AmpCs ((blaFOX-M (64%) and blaDHA-M and blaEDC-M (27%)), ESBLs ((blaCTX-M (81%), other β-lactamase genes blaTEM (73%) and blaSHV (27%)) and carbapenemase ((blaOXA-48 (60%) and blaNDM and blaKPC (40%)) were also detected. One K. pneumoniae co-harbored AmpC (blaFOX-M and blaEBC-M) and carbapenemase (blaKPC and blaOXA-48) genes. blaOXA-48 gene was detected in one carbapenem-resistant Acinetobacter baumannii. Overall, isolates were resistant to a wide range of antimicrobials including last-line treatment options. This underpins the need for continuous surveillance for effective management of infections caused by these pathogens in our settings.