We report mid-infrared (MIR) nonlinear absorption in As2S3 glasses which results from two-photon excitation of valence electron to the Urbach extension followed by strong linear absorption of excited states. The measured MIR nonlinear absorption can be 3 to 4 orders of magnitude stronger than the two-photon absorption in the near-infrared for similar laser intensities and does not result from contaminants, but it is intrinsic to As2S3 glasses. As2S3 fibers are widely used to generate supercontinuum by pumping them with high peak power laser pulses. For a 100 kilowatt peak power MIR soliton propagating in single mode As2S3 fiber, the nonlinear absorption can be of similar magnitude than the fiber background loss. Finally, for laser peak power around 1 MW, the MIR nonlinear absorption can be ~2 orders of magnitude larger than the fiber background loss in single mode As2S3 fiber.