Background This study targets the enhanced production of l-asparaginase, an antitumor enzyme by Acinetobacter baumannii ZAS1. This organism is an endophyte isolated from the medicinal plant Annona muricata. Plackett–Burman design (PBD) and central composite design (CCD) were used for statistical optimization of media components. Results The organism exhibited 18.85 ± 0.2 U/mL enzyme activities in unoptimized media. Eight variables: l-asparagine, peptone, glucose, lactose, yeast extract, NaCl, MgSO4, and Na2HPO4 were screened by PBD. Among them, only four factors—l-asparagine, peptone, glucose, and Na2HPO4—were found to affect enzyme production significantly (p < 0.05). Furthermore, the best possible concentrations and interactive effects of the components that enhance this enzyme's output were chosen by using CCD on these selected variables. The results revealed that an optimized medium produces a higher concentration of enzymes than the unoptimized medium. After optimizing media components, the maximum l-asparaginase activity was 45.59 ± 0.36 U/mL, around the anticipated value of 45.04 ± 0.42 U/mL. After optimization of process parameters, it showed a 2.41-fold increase in the production of l-asparaginase by the endophyte Acinetobacter baumannii ZAS1. Conclusion The findings of this study indicated that an endophyte, Acinetobacter baumannii ZAS1 that produces l-asparaginase could be used to increase enzyme output. However, using the statistical methods Plackett-Burman design and central composite design of response surface methodology is a handy tool for optimizing media components for increased l-asparaginase synthesis.