  Fast spinning magnetars are discussed as strong sources of high energy
neutrinos. Pulsars may be born with a short rotation period of milliseconds
with the magnetic field amplified through dynamo processes up to $\sim
10^{15}-10^{16} \rm G$. As such millisecond magnetars (MSMs) have an enormous
spin-down power $\sim 10^{50} {\rm erg} {\rm s}^{-1}$, they can be potentially
a strong, extragalactic high-energy neutrino source. Specifically, acceleration
of ions and subsequent photomeson production within the MSM magnetosphere are
considered. As in normal pulsars, particle acceleration leads to
electron-positron pair cascades that constrains the acceleration efficiency.
The limit on the neutrino power as a fraction of the spin-down power is
calculated. It is shown that neutrinos produced in the inner magnetosphere have
characteristic energy about a few $\times100$ GeV due to the constraint of
cooling of charged pions through inverse Compton scattering. TeV neutrinos may
be produced in the outer magnetosphere where ions can be accelerated to much
higher energies and the pion cooling is less severe than in the inner
magnetosphere. High energy neutrinos can also be produced from interactions
between ultra-high energy protons accelerated in the magnetosphere and a
diffuse thermal radiation from the ejecta or from the interaction region
between the MSM wind and remnant shell. The detectability of neutrinos in the
early spin-down phase by the current available and planned neutrino detectors
is discussed.
