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We propose a mechanism for magnon-plasmon coupling and hybridization in ferromagnetic (FM) and antiferromagnetic (AFM) systems. The electric field associated with plasmon oscillations creates a non-equilibrium spin density via the inverse spin galvanic effect. This plasmon-induced spin density couples to magnons by an exchange interaction. The strength of magnon-plasmon coupling depends on the magneto-electric susceptibility of the system and the wavevector at which the level repulsion is happened. This wavevector may be tuned by an applied magnetic field. In AFM systems, the degeneracy of two chiral magnons is broken in the presence of a magnetic field, and we find two separate hybrid modes for left-handed and right-handed AFM magnons. Furthermore, we show that magnon-plasmon coupling in AFM systems is enhanced because of strong intra-sublattice spin dynamics. We argue that the recently discovered two-dimensional magnetic systems are ideal platforms to investigate proposed magnon-plasmon hybrid modes.