This paper presents a novel classical algorithm to learn the stabilizer group of a Matrix Product State (MPS). The algorithm uses a biased sampling strategy in the Pauli (Bell) basis to efficiently extract stabilizer generators. The method is benchmarked on T-doped states, showing accurate results even for highly entangled MPS with bond dimension χ ~ 10³. The algorithm has a favorable scaling of O(χ³), enabling the first effective approach to obtain a genuine magic monotone for MPS, facilitating systematic studies of quantum many-body physics out-of-equilibrium. The stabilizer group of a quantum state is the set of Pauli strings that leave the state invariant under their action. For a given MPS, the algorithm samples Pauli strings with a bias towards those in the stabilizer group. This is achieved by iteratively sampling and updating environment matrices, which encode information about previously sampled sites. The algorithm efficiently identifies stabilizer generators, which are independent Pauli strings that generate the stabilizer group. The method is effective for both stabilizer and t-doped states, where t-doped states are obtained by applying a small number of non-Clifford T gates to a stabilizer state. The algorithm's performance is demonstrated on T-doped states, where it successfully identifies the stabilizer group even for large system sizes. The algorithm's efficiency is due to its O(χ³) scaling, making it suitable for MPS with large bond dimensions. The algorithm's output is a set of stabilizer generators and an estimate of the stabilizer dimension of the state. The method is particularly useful for studying non-stabilizerness, a key resource in quantum computing. By identifying the stabilizer group of an MPS, the algorithm enables the development of hybrid MPS-stabilizer techniques, which can reduce the computational complexity of simulating quantum states. The algorithm is implemented using a tensor network approach, where environment matrices are updated iteratively to encode information about previously sampled sites. The algorithm's effectiveness is demonstrated through numerical experiments, where it successfully identifies the stabilizer group of T-doped states with high accuracy. The method's ability to handle large system sizes and high bond dimensions makes it a valuable tool for studying quantum many-body systems.This paper presents a novel classical algorithm to learn the stabilizer group of a Matrix Product State (MPS). The algorithm uses a biased sampling strategy in the Pauli (Bell) basis to efficiently extract stabilizer generators. The method is benchmarked on T-doped states, showing accurate results even for highly entangled MPS with bond dimension χ ~ 10³. The algorithm has a favorable scaling of O(χ³), enabling the first effective approach to obtain a genuine magic monotone for MPS, facilitating systematic studies of quantum many-body physics out-of-equilibrium. The stabilizer group of a quantum state is the set of Pauli strings that leave the state invariant under their action. For a given MPS, the algorithm samples Pauli strings with a bias towards those in the stabilizer group. This is achieved by iteratively sampling and updating environment matrices, which encode information about previously sampled sites. The algorithm efficiently identifies stabilizer generators, which are independent Pauli strings that generate the stabilizer group. The method is effective for both stabilizer and t-doped states, where t-doped states are obtained by applying a small number of non-Clifford T gates to a stabilizer state. The algorithm's performance is demonstrated on T-doped states, where it successfully identifies the stabilizer group even for large system sizes. The algorithm's efficiency is due to its O(χ³) scaling, making it suitable for MPS with large bond dimensions. The algorithm's output is a set of stabilizer generators and an estimate of the stabilizer dimension of the state. The method is particularly useful for studying non-stabilizerness, a key resource in quantum computing. By identifying the stabilizer group of an MPS, the algorithm enables the development of hybrid MPS-stabilizer techniques, which can reduce the computational complexity of simulating quantum states. The algorithm is implemented using a tensor network approach, where environment matrices are updated iteratively to encode information about previously sampled sites. The algorithm's effectiveness is demonstrated through numerical experiments, where it successfully identifies the stabilizer group of T-doped states with high accuracy. The method's ability to handle large system sizes and high bond dimensions makes it a valuable tool for studying quantum many-body systems.