Combine the carrot juice, orange juice, orange zest, and icing sugar in a bowl.
Filter the mixture and pour it into the popsicle moulds and place in the freezer to freeze overnight. If you are adding wooden sticks to your ice blocks (instead of using the popsicle holder tops), then add them about 2 hours after they go into the freezer. This way the liquid will be icy enough to keep them upright.