The origin of the narrow Fe-Kα 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 ∼5 eV at 6 keV achieved by Hitomi/SXS, we detected the Fe-Kα line with ∼5.4 σ 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 ∼20 keV, giving an equivalent width of ∼20 eV for the 6.4 keV line. Because the velocity width is narrower than that of the broad Hα line of ∼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-Kα line comes from a region within ∼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-Kα 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.