Magnetic topological insulators can host chiral 1D edge channels at zero magnetic field, when a magnetic gap opens at the Dirac point in the band structure of 2D topological surface states, leading to the quantum anomalous Hall effect in ultrathin nanostructures. For thicker nanostructures, quantization is severely reduced by the coexistence of edge states with other quasi-particles, usually considered as bulk states. Yet, surface states also exist above the magnetic gap, but it remains difficult to identify electronic subbands by electrical measurements due to strong disorder. Here we unveil surface states in MnBi₂Te₄ nanostructures, using magneto-transport in very-high magnetic fields up to 55 T, giving evidence of Shubnikov-de-Haas oscillations above 40 T. A detailed analysis confirms the 2D nature of these quantum oscillations, thus establishing an alternative method to photoemission spectroscopy for the study of topological surface states in magnetic topological insulators using Landau level spectroscopy.