We report on a signature indicating a transition to the orbital-selective Mott phase in superconducting ${\mathrm{K}}_{x}$${\mathrm{Fe}}_{2\ensuremath{-}y}$${\mathrm{Se}}_{2}$ single crystals by employing dual-color pump-probe spectroscopy. In addition to the multiexponential-decay recovery dynamics of photoinduced quasiparticles, a damped oscillatory component caused by coherent acoustic phonons emerges when the superconducting phase is suppressed at an increased temperature or excitation power. Upon raising the temperature to 150--170 K, the oscillatory component diminishes alongside a significant enhancement of the slow decay component in the recovery traces. These results can be understood as a gap opening in certain $k$ directions, indicating that a vital role is played by electron correlation in iron-based superconductors.