We have carried out75As 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~ 45 K. In the superconducting (SC) state, the NMR signal intensity decreases suddenly just below Tc~ 20 K due to Meissner effect, evidencing the coexistence of the hedgehog SVC AFM and SC states from a microscopic point of view.