The dynamics of the icosahedral ZnMgY phase has been investigated on a single-grain quasicrystalline sample using inelastic neutron scattering. Similarly to other quasicrystals we observe well-defined acoustic modes for values of the wavevector smaller than 0.3 Å-1. We find that transverse excitations remain acoustic up to q=0.5 Å-1. For q lying between 0.3 and 0.5 Å-1 we observe a broadening, which is independent of the propagation or polarisation direction, while the dispersion relation departs from linearity. For q=0.6 Å-1 there is a resonance with an optic-like excitation located at about 10 meV and the signal can no longer be described by a single acoustic mode. For larger wavevectors we observe a broad distribution of modes which can be split into three dispersionless optical bands located at 8, 12 and 17 meV. The first two bands are associated with the crossing of the pseudo-zone boundary by the acoustic branch.