  We report a first theoretical study for neutrino-induced diffractive
productions of heavy pseudoscalar mesons, \eta_c and \eta_b, off a nucleon.
Based on factorization formalism for exclusive processes, we evaluate the
forward diffractive production cross section in perturbative QCD in terms of
the light-cone Q\bar{Q} wave functions (WFs) of \eta_{c,b} mesons and the gluon
distribution of the nucleon. The light-cone WFs of the \eta_c (\eta_b) meson
are constructed to satisfy the spin symmetry relations with those of the J/\psi
(\Upsilon) meson. The diffractive \eta_c production is governed by the
axial-vector coupling of the longitudinally polarized Z boson to Q\bar{Q} pair,
and the resulting \eta_c production rate is larger than the J/\psi one by one
order of magnitude. We also discuss the production of bottomonium \eta_b, which
shows up for higher beam energy.
