The theory of free-carrier absorption (FCA) is given for monolayers of transition-metal dichalcogenides, particularly for molybdenum disulphide (MoS2), when carriers are scattered by phonons. Explicit expressions for the absorption coefficient α are obtained and discussed for acoustic phonon scattering via screened deformation potential and piezoelectric coupling taking polarization of the radiation in the plane of the layer. It is found that α monotonously decreases with the increasing photon frequency Ω, increases with the increasing temperature T, and linearly depends on two-dimensional electron concentration ns. Effect of screening, which is ignored in all the earlier FCA studies, is found to reduce α significantly, attributing to the larger effective mass of the electrons. Results are also obtained in the classical and quantum limit giving the power laws α ∼ Ω−2 and T. Comparison of the results is made with those in bulk semiconductors and semiconductor quantum wells.