The significance of this paper is an investigation into the design, development, and optimization of a new polymeric hybrid auxetic structure by additive manufacturing (AM). This work will introduce an innovative class of polymeric hybrid auxetic structure by the integration of an arrow-head unit cell into a missing rib unit cell, which will be fabricated using fused filament fabrication (FFF) technique, that is, one subset of AM. The auxetic performance of the structure is validated through the measurement of its negative Poisson’s ratio, confirming its potential for enhanced energy absorption. A chain of regression, linear, and quadratic polynomial machine learning algorithms are used to predict and optimize the energy absorption capability at variant processing conditions. Amongst them, the polynomial regression model stands out with an R-squared value of 92.46%, reflecting an excellent predictive capability for energy absorption of additively manufactured polymeric hybrid auxetic structure. The optimization technique revealed that the printing speed of 80 mm/s and layer height of 200 µm were the critical values to achieve a maximum amount of energy absorption at 5.954 kJ/m2, achieved at a printing temperature of 244.65 °C. Such results also contribute to the development of AM, since they show not only the potential for energy absorption of polymeric hybrid auxetic structures but also how effective machine learning is in the optimization of the AM process.