We investigated the infrared optical spectra of an organic dimer Mott insulator kappa-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl, which was irradiated with x rays. We observed that the irradiation caused a large spectral weight transfer from the midinfrared region, where interband transitions in the dimer and Mott-Hubbard bands take place, to a Drude part in a low-energy region; this caused the Mott gap to collapse. The increase of the Drude part indicates a carrier doping into the Mott insulator due to irradiation defects. The strong redistribution of the spectral weight demonstrates that the organic Mott insulator is very close to the phase border of the bandwidth-controlled Mott-insulator-metal transition.