We numerically study the dynamics of quantum entanglement between interacting electron-phonon and qubit-spin systems under photoirradiation, employing a model of multiple spins and boson modes. The interplay of the antiferromagnetic exchange and electron-phonon interactions provides us with a phase diagram, wherein each phase is characterized by the ground state property of the electron-phonon system. Light irradiation of the electron-phonon system facilitates the generation of quantum entanglement, according to the spin configuration and the phonon state in the ground state. Analyses using the quantum mutual information and the singular values of the reduced density matrix indicate that the quantum mechanical effect of the irradiated light appears in the state of the material.