The specific polarization of radially polarized lasers with cylindrical structures and longitudinal electric fields at their focal spots are of interest, as are the fundamental characteristics of electromagnetic (EM) solitons. Compared with linearly and circularly polarized lasers, radially polarized lasers have a more perfect symmetry, which makes them more suitable for studying the topological structure in laser–plasma interaction. We report the structural features of EM solitons induced via a radially polarized laser on the basis of three-dimensional particle-in-cell simulations. It has been discovered that a fractal-like structure is produced due to the interaction between the radially polarized laser and the plasma, and that this structure indirectly originates from the Weibel instability of the electron ring. This novel regime will allow potential applications such as the manipulation of relativistic electrons, mode filtering, and fractal-like particle acceleration.