  In this work, the mass of the neutral pion is investigated in the presence of
background magnetic fields in the framework of the Nambu--Jona-Lasinio model.
Taking into account the anisotropic four-fermion interactions, a tensor current
arises in the magnetized QCD system, which forms an anomalous magnetic moment
(AMM) coupling in the Dirac equation for the quarks. By solving the gap
equations, we find that the sign of the dynamically generated AMM is opposite
to the sign of the quark's charge and its magnitude is definitely smaller than
the constituent mass. We construct two generalized Nambu-Goldstone pions, which
emerge as combinations of the quantum fluctuations around the conventional
scalar and the emergent tensor chiral condensates. We analytically demonstrate
that the Goldstone nature has been spoiled by the dimensional reduction in the
two-particle state and the corresponding decreasing mass of the lighter
generalized pionic mode is a remnant of the infrared dynamics.
