The aim of this study was to study the molecular epidemiology of 16S rRNA-methylase (RMT)-producing clinical Acinetobacter baumannii isolates from hospitals in Athens, Greece. Single-patient A. baumannii clinical isolates, coresistant to amikacin and gentamicin (n = 347), from five tertiary care hospitals, were submitted to minimum inhibitory concentration determination and molecular testing for carbapenemase and RMT genes. A. baumannii, resistant to amikacin and gentamicin, was isolated at participating institutions at a mean rate of 67.8%. Among them 93.7% harbored the armA. The vast majority (98.5%) of armA positive isolates were OXA-23 producers, assigned mainly (99.4%) to sequence group G1, corresponding to international clone (IC) II. Four isolates (all from the same hospital) were OXA-24 producers (1.2%), assigned to G6 corresponding to CC78 and only one isolate was OXA-58-producer, assigned to G2 (IC I). Apramycin was the most active agent inhibiting 99.7% of the isolates at ≤64 mg/L, whereas colistin, trimethoprim/sulfamethoxazole, minocycline, and tigecycline exhibited only sparse activity (S, <18%). RMT production is an emerging mechanism of resistance, capable of compromising the clinical efficacy of aminoglycosides. High prevalence of armA was observed among A. baumannii strains isolated in participating hospitals in Athens, which were mainly OXA-23 producers and belonged to IC II. Apramycin is a structurally unique aminoglycoside, currently used as a veterinary agent. Although it has not been evaluated for clinical use, apramycin appears worthy of further investigation for repurposing as a human therapeutic against difficult-to-treat pathogens.