We have calculated the complete electroweak O(alpha) radiative corrections to the single Higgs-boson production processes e+ e- --> nu_l anti-nu_l H (l=e,mu,tau) in the electroweak Standard Model. Initial-state radiation beyond O(alpha) is included in the structure-function approach. The calculation of the corrections is briefly described, and numerical results are presented for the total cross section. In the G_mu scheme, the bulk of the corrections is due to initial-state radiation, which affects the cross section at the level of -7% at high energies and even more in the ZH threshold region. The remaining bosonic and fermionic corrections are at the level of a few per cent. The confusing situation in the literature regarding differing results for the fermionic corrections to this process is clarified.