Salinity, a severe worldwide issue, compromises the economic production of medicinal plants including mints and causes drug-yield decline. γ-Aminobutyric acid (GABA) is a tolerance-inducing signaling bio-molecule in various plant physiological processes. Pineapple mint (Mentha suaveolensEhrh.) is a valuable medicinal herb with an exhilarating scent of citrus fruit. Piperitenone oxide is the major bioactive constituent of its essential oil, having significant demand by pharmaceutical industries. Nonetheless, modeling and optimizing the effective concentration of GABA remain within twin foci of interest. Therefore, a two factor-five level (NaCl 0-150 mM and GABA 0-2.4 mM) central composite design was conducted to model and optimize drug yield and physiological responses ofM.suaveolens. Based on the design of experiments (DoE) approach, different linear, quadratic, cubic, and quartic models were assigned to the response variables. Change trends of shoot and root dry weights followed a simple linear model, whereas sophisticated models (i.e., multiple polynomial regression) were fitted to the other traits. NaCl stress inevitably reduced root and shoot dry weight, piperitenone oxide content, relative water content, pigments content, and maximum quantum yield of PSII. However, content of malondialdehyde (MDA) and total flavonoid, and DPPH radical scavenging activity were increased under salinity. Under severe NaCl stress (150 mM), the essential oil content (0.53%) was increased three times in comparison with control (0.18%). Optimization analysis demonstrated that the highest amount of essential oil (0.6%) and piperitenone oxide (81%) as a drug yield-determining component would be achievable by application of 0.1–0.2 mM GABA under 100 mM NaCl. The highest dry weight of root and shoot was predicted to be achieved at 2.4 mM GABA. Overall, extremely severe NaCl stress (i.e., more than 100 mM) in which a sharp drop in yield components value was observed seemed to be out ofM. suaveolenssalinity tolerance range. Hence, it is rationale to compensate the decrease of drug yield by foliar application of a dilute GABA solution (i.e., 0.1–0.2 mM) under 100 mM NaCl stress or lower levels.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12870-023-04312-w.