We use the linear sigma model coupled to quarks with an explicit symmetry breaking term, to compute the one-loop magnetic modification of the neutral pion mass, in the weak field approximation. The self-energy, the effective, and the meson self-coupling are computed at one-loop order. We obtain a decreasing behavior for the neutral pion mass as the magnetic field increases. This result is in good agreement both with other effective models and lattice quantum chromodynamics (QCD) results.