The LIGO/Virgo detected a gravitational wave (GW) event, named GW200224_222234 (also known as S200224ca) and classified as a binary-black hole coalescence, on 2020 February 24. Given its relatively small localization skymap (71 deg2 for a 90% credible region; revised to 50 deg2 in GWTC-3), we performed target-of-opportunity observations using the Subaru/Hyper Suprime-Cam (HSC) in the r2 and z bands. Observations were conducted on 2020 February 25 and 28 and March 23, with the first epoch beginning 12.3 hr after the GW detection. The survey covered the highest-probability sky area of 56.6 deg2, corresponding to a 91% probability. This was the first deep follow-up (m r ≳ 24, m z ≳ 23) for a binary-black hole merger covering >90% of the localization. By performing image subtraction and candidate screening including light-curve fitting with transient templates and examples, we found 22 off-nucleus transients that were not ruled out as the counterparts of GW200224_222234 with our Subaru/HSC data alone. We also performed GTC/OSIRIS spectroscopy of the probable host galaxies for five candidates; two are likely to be located within the 3D skymap, whereas the others are not. In conclusion, 19 transients remain as possible optical counterparts of GW200224_222234; but we could not identify a unique promising counterpart. If there are no counterparts in the remaining candidates, the upper limits of the optical luminosity are $\nu {L}_{\nu }\lt {5.2}_{-1.9}^{+2.4}\times {10}^{41}$ erg s-1 and $\nu {L}_{\nu }\lt {1.8}_{-0.6}^{+0.8}\times {10}^{42}$ erg s-1 in the r2 and z bands, respectively, at ~12 hr after GW detection. We also discuss improvements in the strategies of optical follow-ups for future GW events.