  We show that measuring the velocity components of hypervelocity stars (HVSs)
can discriminate between Modified Newtonian Dynamics (MOND) and Newtonian
gravity. HVSs are ejected from the Galactic center on radial trajectories with
a null tangential velocity component in the reference frame of the Galaxy. They
acquire tangential components due to the non-spherical components of the
Galactic gravitational potential. Axisymmetric potentials only affect the
latitudinal components $v_\theta$, and non-null azimuthal components $v_\phi$
originate from non-axisymmetric matter distributions. For HVSs with
sufficiently large ejection speed, the azimuthal velocity components are
proportionate to the deviation of the gravitational potential from axial
symmetry. The ejection velocity threshold is $\sim$ 750 km s$^{-1}$ for 4
$M_{\odot}$ stars and increases with decreasing HVS mass. We determine the
upper limit of $v_\phi$ as a function of the Galactocentric distance for these
high-speed HVSs, if MOND, in its QUMOND formulation, is the correct theory of
gravity and the triaxial Galactic bulge is the primary source of the azimuthal
component $v_\phi$. In Newtonian gravity, values of $v_\phi$ larger than this
limit can easily appear if the dark matter halo is triaxial or if the dark
matter halo and the baryonic components are axisymmetric but their two axes of
symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs
could in principle distinguish between the QUMOND scenario and the dark matter
model if the azimuthal components $v_\phi$ of the observed HVSs do not meet the
QUMOND upper limit. However, the uncertainties on the Galactocentric azimuthal
velocity components of the currently known HVSs are still at least a factor of
$\sim 10$ too large to make this test conclusive. Astrometric measurements with
micro-arcsecond precision would make this test feasible.
