A high-resolution micro channel-cut crystal monochromator (µCCM) composed of an Si(220) crystal is developed for the purpose of narrowing the bandwidth of a reflection self-seeded X-ray free-electron laser. Subsurface damage on the monochromator, which distorts the wavefront and broadens the bandwidth of the monochromatic seed beam, was removed by using a plasma etching technique. High diffraction performance of the monochromator was confirmed through evaluation with coherent X-rays. Reflection self-seeding operation was tested with the Si(220) µCCM at SPring-8 Angstrom Compact free-electron laser. A narrow average bandwidth of 0.6 eV, which is five times narrower than the value previously reported [I. Inoue et al., Nat. Photonics 13, 319 (2019)], was successfully obtained at 9 keV. The narrow-band X-ray beams with high intensity realized in this study will further expand the capabilities of X-ray free-electron lasers.