The Arctic Marginal Ice Zone (MIZ), where strong interactions between sea ice, ocean and atmosphere are taking place, is expanding as the result of the on-going sea ice retreat. Yet, state-of-art models are not capturing the complexity of the varied processes occurring in the MIZ, and in particular the processes involved in the ocean-sea ice interactions. In the present study, a coupled sea ice - wave model is developed, in order to improve our understanding and model representation of those interactions. The coupling allows us to account for the wave radiative stress resulting from the wave attenuation by sea ice, and the sea ice lateral melt resulting from the wave-induced sea ice break-up. We found that, locally in the MIZ, the waves can affect the sea ice drift and melt, resulting in significant changes in sea ice concentration and thickness as well as sea surface temperature and salinity. Our results highlight the need to include the wave-sea ice processes in models aiming at forecasting sea ice conditions on short time scale, although the coupling between waves and sea ice would probably required to be investigated in a more complex system, allowing for interactions with the ocean and the atmosphere.