The origin of the narrow Fe-K alpha fluorescence line at 6.4 keV from active galactic nuclei has long been under debate; some of the possible sites are the outer accretion disk, the broad line region, a molecular torus, or interstellar/intracluster media. In 2016 February-March, we performed the first X-ray microcalorimeter spectroscopy with the Soft X-ray Spectrometer (SXS) on board the Hitomi satellite of the Fanaroff-Riley type I radio galaxy NGC 1275 at the center of the Perseus cluster of galaxies. With the high-energy resolution of similar to 5 eV at 6 keV achieved by Hitomi/SXS, we detected the Fe-K alpha line with similar to 5.4 sigma significance. The velocity width is constrained to be 500-1600 km s(-1) (FWHM for Gaussian models) at 90% confidence. The SXS also constrains the continuum level from the NGC 1275 nucleus up to similar to 20 keV, giving an equivalent width of similar to 20 eV for the 6.4 keV line. Because the velocity width is narrower than that of the broad H alpha line of similar to 2750 km s(-1), we can exclude a large contribution to the line flux from the accretion disk and the broad line region. Furthermore, we performed pixel map analyses on the Hitomi/SXS data and image analyses on the Chandra archival data, and revealed that the Fe-K alpha line comes from a region within similar to 1.6 kpc of the NGC 1275 core, where an active galactic nucleus emission dominates, rather than that from intracluster media. Therefore, we suggest that the source of the Fe-K alpha line from NGC 1275 is likely a low-covering-fraction molecular torus or a rotating molecular disk which probably extends from a parsec to hundreds of parsecs scale in the active galactic nucleus system.