In the container of a food processor or blender, combine blueberries and apple juice concentrate; whirl until liquefied. Pour into an 11 x 7-inch baking pan. Cover and freeze until firm around the edges, about 2 hours.

With a heavy spoon, break frozen mixture into pieces. Place mixture in a processor or blender container; whirl until smooth but not completely melted.

Spoon into a 9 x 5-inch loaf pan; cover and freeze until firm. Serve within a few days.