We report a novel superconducting (SC) and antiferromagnetic (AF) hybrid state in SrFe(2)As(2) revealed by (75)As nuclear magnetic resonance (NMR) experiments on a single crystal under highly hydrostatic pressure up to 7 GPa. The NMR spectra at 5.4 GPa indicate simultaneous development of the SC and AF orders below 30 K. The nuclear spin-lattice relaxation rate in the SC domains shows a substantial residual density of states, suggesting proximity effects due to the spontaneous formation of a nanoscale SC-AF hybrid structure. This entangled behavior is a remarkable example of a self-organized heterogeneous structure in a clean system.