Auxetic lattices are being explored for diverse industrial applications. Numerical homogenization offers a way to obtain effective material properties of a lattice structure without the necessity of intricate modeling for the entire lattice. In this study, a finite element approach is applied to a representative volume element of a re-entrant honeycomb auxetic lattice to determine equivalent solid properties via parametric tuning. To enhance computational efficiency, the machine learning technique is integrated with computational data for the prediction of effective elastic properties of auxetic honeycomb lattices of any configuration. Six machine learning-based algorithms were utilized to validate the outcomes derived from finite element homogenization. The machine learning model inputs the auxetic honeycomb design parameters and predicts the equivalent solid mechanical properties as output. The analysis revealed that the random forest algorithm emerged as the most effective machine learning model based on the finite element homogenization data. They exhibited remarkable consistency in replicating the test set trends and displayed a low validation mean absolute percentage error. The notion that changing the design parameters of an auxetic honeycomb has a perceptible impact on its effective elastic response is underlined by these predictions made by the trained algorithms, eliminating the need for costly computational methods.