The coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by an 75 As nuclear magnetic resonance study on single-crystalline CaK ( Fe 0.951 Ni 0.049 ) 4 As 4 . The hedgehog SVC order is clearly demonstrated by the direct observation of internal magnetic induction along the c axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature T N ∼ 52 K. The nuclear spin-lattice relaxation rate 1 / T 1 shows a distinct decrease below T c ∼ 10 K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the 1 / T 1 data, the hedgehog SVC-type spin correlations are found to be enhanced below T ∼ 150 K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor.