Light enables ultrafast, direct and nonthermal control of the exchange and Dzyaloshinskii-Moriya interactions. We consider two-dimensional honeycomb lattices described by the Kane-Mele-Hubbard model at half filling and in the strongly correlated limit, i.e., the Mott insulator regime of a canted antiferromagnet. Based on Floquet theory, we demonstrate that by changing the amplitude and frequency of polarized laser pulses, one can tune the amplitudes and signs of and even the ratio between the exchange and Dzyaloshinskii-Moriya spin interactions. Furthermore, the renormalizations of the spin interactions are independent of helicity. Our results pave the way for ultrafast optical spin manipulation in recently discovered two-dimensional magnetic materials.