We consider the Fröhlich Hamiltonian for a polaron in a constant magnetic field, which is translation invariant in the z-direction. For weak magnetic field strengths, we show that the low-lying spectra of the corresponding fiber Hamiltonians for fixed, sufficiently small total momenta in the z-direction approximately have Landau level structures. The spacing of the Landau levels is determined by the renormalized polaron mass. A key technique in the proof, borrowed from the theory of periodic Schrödinger operators coupled to weak magnetic fields, is the construction of an effective Hamiltonian acting in the sub-Hilbert space generated by a system of magnetic quasi-Wannier functions for the polaron. The talk is based on joint work with Horia Cornean und Rohan Ghanta.