When the juice freezes it will expand, which might burst the container. I'm not if this will happen, it will probably depend on the type of container and whether there is much space in it to allow expansion. You could try it out anyway, and see what happens. But worth checking if the container is burst before it melts.
Talyn, I've read freezing food in some plastic bags causes the food to absorb bad chemicals, like pthalates. I don't know if this is pseudo-science or not, I'm not an expert on the distinction. Some scientific claims and pseudo-scientific claims seem to overlap, and I don't have it all sorted out yet. I just ask questions to get different opinions and try to make my best judgement.