  We investigate the effects of the transitional magnetic dipole moment of the
active-to-heavy-neutrino associated with a new neutral gauge boson $Z'$ on
neutrino-nucleon scattering at the ForwArd Search ExpeRiment-$\nu$
(FASER$\nu$). We consider the neutral-current neutrino-nucleon scattering ($\nu
A\rightarrow N A$) as the production mechanism of the heavy neutrino $N$ at
FASER$\nu$ and estimate the sensitivity reach on the magnetic moment coupling
$\mu_{\nu_\alpha}$ for a range of heavy neutrino mass ($1\,{\rm GeV} < M_{N} <
70 {\rm GeV}$). In this study, we consider three benchmark models, in which the
heavy neutrino is coupled to $L_e$, $L_\mu$ or $L_\tau$ doublet, respectively.
