Carbapenem-resistant Acinetobacter baumannii is one of the major problems among hospitalized patients. The presence of multiple virulence factors results in bacteria persistence in the hospital environment. It facilitates bacterial transmission between patients, causing various types of infections, mostly ventilator-associated pneumonia and wound and bloodstream infections. A. baumannii has a variable number of resistance mechanisms, but the most commonly produced are carbapenem-hydrolyzing class D β-lactamases (CHDLs). In our study, the presence of blaOXA-23, blaOXA-40 and blaOXA-51 genes was investigated among 88 clinical isolates of A. baumannii, including 53 (60.2%) strains resistant to both carbapenems (meropenem and imipenem) and 35 (39.8%) strains susceptible to at least meropenem. Among these bacteria, all the isolates carried the blaOXA-51 gene. The blaOXA-23 and blaOXA-40 genes were detected in two (5.7%) and three (8.6%) strains, respectively. Among the OXA-23 carbapenemase-producing A. baumannii strains (n = 55), insertion sequences (ISAba1) were detected upstream of the blaOXA-23 gene in fifty-two (94.5%) carbapenem-resistant and two (3.6%) meropenem-susceptible isolates. A. baumannii clinical strains from Poland have a similar antimicrobial resistance profile as those worldwide, with the presence of ISAba1 among blaOXA-23-positive isolates also being quite common. Carbapenem resistance among A. baumannii strains is associated with the presence of CHDLs, especially when insertion sequences are present.