Magnetic topological insulators exhibit unique electronic states due to the interplay between the electronic topology and the spin structure. The antiferromagnetic metal EuIn2As2 is a prominent candidate material in which exotic topological phases, including an axion insulating state, are theoretically predicted depending on the magnetic structure of the Eu2+ moments. Here, we report experimental results of the nuclear magnetic resonance (NMR) measurements of all the nuclei in EuIn2As2 to investigate the coupling between the magnetic moments in the Eu ions and the conduction electrons in In2As2 layers and the magnetic structure. The 75As and 115In NMR spectra observed at zero external magnetic fields reveal the appearance of internal fields of 4.9 and 3.6 T, respectively, at the lowest temperature, suggesting a strong coupling between the conduction electrons in the In2As2 layer and the ordered magnetic moments in the Eu ions. The 75As NMR spectra under in-plane external magnetic fields show broad distributions of the internal fields produced by an incommensurate fan-like spin structure which turns into a forced ferromagnetic state above 0.7 T. We propose a spin reorientation process that an incommensurate helical state at zero external magnetic field quickly changes into a fan state by applying a slight magnetic field.