  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 nonspherical 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 high ejection speed, $v_\phi$ is proportionate to the deviation of
the gravitational potential from axial symmetry. The ejection velocity
threshold is $\sim$ 750 km/s 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 QUMOND, the
quasi-linear formulation of MOND, is the correct theory of gravity and either
the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary
source of $v_\phi$. In Newtonian gravity, the HVSs within 60 kpc of the
Galactic center may easily have $v_\phi$ values higher than the QUMOND upper
limit if the dark matter (DM) halo is triaxial or if the DM 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
distinguish between QUMOND and the DM model. This test is currently limited by
(i) the lack of a proper procedure to assess the HVS nature of a star in the
model to be constrained; and (ii) the present uncertainties on $v_\phi$, which
are a factor of $\sim 10$ too large. A proper procedure to assess the HVS
nature of the stars and astrometric measurements with microarcsecond precision
would make this test feasible.
