In what we consider true "cannon" of star trek (tv show/movies), this is not answered. In the lower tiers of cannon it was answered in the star trek online mmo. In sto this and another dyson sphere were created by a race called the solangae, we also have instances in game of dyson spheres being created by the iconians. http://en.memory-alpha.org/wiki/Dyson_sphere

In what we consider true "canon" of star trek (tv show/movies), this is not answered. In the lower tiers of cannon it was answered in the star trek online mmo. In sto this and another dyson sphere were created by a race called the solangae, we also have instances in game of dyson spheres being created by the iconians. http://en.memory-alpha.org/wiki/Dyson_sphere