Background: Multidrug resistance in Gram-negative pathogens like Klebsiella pneumoniae and Enterobacter species (spp.) poses a major challenge in the management of chronic wounds, especially in diabetic patients. This study aimed to isolate and identify Klebsiella and Enterobacter spp. from chronic wound patients in a tertiary hospital in Southwest Nigeria and determine the antibiotic resistance pattern of the recovered isolates. Methods: A total of 165 diabetic and other chronic wound swabs were collected and analyzed. Bacterial isolates were identified using API 20E identification kit and confirmed by polymerase chain reaction (PCR) using genus and species-specific primers. Antibiotic susceptibility testing (AST) was done using the Kirby-Bauer disc diffusion method. Results: Diabetic foot ulcers were the most prevalent at 32.7%; followed by traumatic wounds (23.6%). Eighty-seven isolates were identified as either Klebsiella or Enterobacter spp. The predominant species recovered was Klebsiella spp. at 75.9% (66/87); while Enterobacter spp. was 24.1%. The highest resistance rate was towards nitrofurantoin, ampicillin, and amoxicillin at 97.7% each while the least resistance was to amikacin at 18.4%. Sixteen Klebsiella species, six of them pneumoniae were found to be extremely drug-resistant (XDR). The multiple antibiotics resistance indices revealed that 98.9% of the isolates were ≥ 0.2. Conclusions: The presence of MDR and even XDR strains in chronic wounds is extremely bothersome and is a cause of impending catastrophe in therapeutic options open to clinicians. Hence, an urgent need for a continuous search for viable alternative therapies and a dynamic surveillance program to monitor and tackle this challenge is required.