We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called "type-II fracton topological states." The main challenge in realizing fractonlike models in standard condensed matter platforms is the creation of multispin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.