The origin of the electronic nematicity in FeSe is one of the most important unresolved puzzles in the study of iron-based superconductors. In both spin- and orbital-nematic models, the intrinsic magnetic excitations at Q₁= (1, 0) and Q₂= (0, 1) of twin-free FeSe are expected to provide decisive criteria for clarifying this issue. Although a spin-fluctuation anisotropy below 10 meV between Q₁ and Q₂ has been observed by inelastic neutron scattering at low temperature, it remains unclear whether such an anisotropy also persists at higher energies and associates with the nematic transition T_s. Here we use resonant inelastic X-ray scattering to probe the high-energy magnetic excitations of detwinned FeSe. A prominent anisotropy between the magnetic excitations along the H and K directions is found to persist to E ≈ 200 meV, which decreases gradually with increasing temperature and finally vanishes at a temperature around T_s. The measured high-energy spin excitations are dispersive and underdamped, which can be understood from a local-moment perspective. Taking together the large energy scale far beyond the d_xz/d_yz orbital splitting, we suggest that the nematicity in FeSe is probably spin-driven.