  In this work, we consider the possible presence of a large population of
millisecond pulsars in the Galactic Centre. Their direct detection would be
challenging due to severe pulse broadening caused by scattering of radiation.
We propose a new method to constrain their population with neutrino imaging of
the Galactic Centre. Millisecond pulsars are proposed cosmic-ray accelerators.
The high-energy protons they produce will collide with the baryonic matter in
the central molecular zone to create charged and neutral pions that decay into
neutrinos and $\gamma$-rays, respectively. The specific neutrino and
$\gamma$-ray fluxes must be below their corresponding observed values, allowing
us to put a conservative upper limit on the millisecond pulsar population of
N_MSP < 10,000 within a galacto-centric radius of 20 pc. This upper limit is
sensitive to the proton acceleration efficiency of the pulsars, but is less
dependent on the particle injection spectral index and the choice of mass
tracers. The population will be better constrained when high resolution
neutrino observations of the Galactic Centre become available. The presence of
these millisecond pulsars can account for the $\gamma$-ray excess in the
Galactic Centre.
