A microscopic model describing interaction between photoinjected carriers and optical phonons in monolayer transition-metal dichalcogenides (2D directbandgap semiconductors) is proposed. The model takes account of the spin-valley structure of the conduction and valence bands. The evolution equations for the carrier and phonon quasitemperatures are derived and the carrier-phonon relaxation time is estimated. The theoretically obtained value of carrier-phonon relaxation times is found to be of the same order of magnitude as for many other 2D highly photoexcited polar semiconductors.