We study the transport properties of a monolayer transition-metal dichalcogenide (TMDC) ribbon subject to a time-periodic circularly polarized laser field. First, we calculate the quasienergy spectrum within the framework of the Floquet theory and analyze the nontrivial topology of the Floquet bulk gaps. The latter is revealed by the presence of chiral edge states inside the bulk gaps in finite samples, in agreement with the calculation of the appropriate winding numbers as a function of both the energy and the amplitude of the laser field. The effect of the time-dependent perturbation on the equilibrium edge states is also analyzed. Finally, we calculate the two-terminal conductance and discuss how the above mentioned effects manifest on it. In particular, besides the expected suppression of the bulk conductance and the emergence of edge transport at the Floquet gaps, we find that there is an asymmetry between left and right transmission coefficients (in the zigzag case), leading to pumping effects. In addition, we found that the laser field can lead to a complete switch off of the linear conductance when the latter is dominated by the equilibrium edge states.