We have carried out 75As nuclear magnetic resonance (NMR) measurements to investigate a new antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC) in CaK(Fe0.967Ni0.033)4As4. 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 of TN approximately 45 K. In the superconducting (SC) state, the NMR signal intensity decreases suddenly just below Tc approximately 20 K due to Meissner effect, evidencing the coexistence of the hedgehog SVC AFM and SC states from a microscopic point of view.