Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition (PT), the magnetically doped topological insulator thin film also undergoes a magnetic PT from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying on change of topology. Our discoveries deepen the understanding of the relationship between topology and magnetism in the non-equilibrium regime and extend optoelectronic device applications to topological materials.