Stem-cell (SC) chirality or left-right (LR) asymmetry is an essential attribute, observed during tissue regeneration. The ability to control the LR orientation of cells by biophysical manipulation is a promising approach for recapitulating their inherent function. Despite remarkable progress in tissue engineering, the development of LR chirality in SCs has been largely unexplored. Here, we demonstrate the role of substrate stiffness on the LR asymmetry of cultured mesenchymal stem cells (MSCs). We found that MSCs acquired higher asymmetricity when cultured on stiffer PCL/collagen matrices. To confirm cellular asymmetry, different parameters such as the aspect ratio, orientation angle and intensity of polarized proteins (Par) were investigated. The results showed a significant (p < 0.01) difference in the average orientation angle, the cellular aspect ratio, and the expression of actin and Par proteins in MSCs cultured on matrices with different stiffnesses. Furthermore, a Gaussian support-vector machine was applied to classify cells cultured on both (2% and 10% PCL/Collagen) matrices, with a resulting accuracy of 96.2%. To the best of our knowledge, this study is the first that interrelates and quantifies MSC asymmetricity with matrix properties using a simple 2D model.