Density functional theory was used to study structural and dynamical changes related to the magnetostructural phase transition in MnAs. The soft mode inducing the transition from the high-symmetry hexagonal to the low-symmetry orthorhombic phase was revealed. A giant coupling between the soft mode and magnetic moments was found and its crucial role in the magnetostructural transition was established. The estimated phonon contribution to the total entropy change has the opposite sign to the magnetic entropy change.