The paper presents a novel classical algorithm designed to learn the stabilizer group of a given Matrix Product State (MPS). The algorithm employs biased sampling in the Pauli (or Bell) basis to efficiently extract the stabilizer generators, which are the Pauli strings for which the state is a ±1 eigenvector. The output is a set of independent stabilizer generators, and the total number of these generators is associated with the stabilizer multiplicity, a well-established nonstabilizer monotone. The method is benchmarked on $T$-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly entangled MPS with bond dimension $\chi \sim 10^3$. The algorithm's computational complexity is favorable, scaling as $\mathcal{O}(\chi^3)$, making it the first effective approach to obtain a genuine magic monotone for MPS. This method enables systematic investigations of quantum many-body physics out-of-equilibrium and has potential applications in reducing the computational complexity of MPS representations.The paper presents a novel classical algorithm designed to learn the stabilizer group of a given Matrix Product State (MPS). The algorithm employs biased sampling in the Pauli (or Bell) basis to efficiently extract the stabilizer generators, which are the Pauli strings for which the state is a ±1 eigenvector. The output is a set of independent stabilizer generators, and the total number of these generators is associated with the stabilizer multiplicity, a well-established nonstabilizer monotone. The method is benchmarked on $T$-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly entangled MPS with bond dimension $\chi \sim 10^3$. The algorithm's computational complexity is favorable, scaling as $\mathcal{O}(\chi^3)$, making it the first effective approach to obtain a genuine magic monotone for MPS. This method enables systematic investigations of quantum many-body physics out-of-equilibrium and has potential applications in reducing the computational complexity of MPS representations.