  Recent measurements performed with some direct dark matter detection
experiments, e.g. CDMS-II and CoGENT (after DAMA/LIBRA), have unveiled a few
events compatible with weakly interacting massive particles. The preferred mass
range is around 10 GeV, with a quite large spin-independent cross section of
$10^{-43}$-$10^{-41}\,{\rm cm^2}$. In this paper, we recall that a light dark
matter particle with dominant couplings to quarks should also generate
cosmic-ray antiprotons. Taking advantage of recent works constraining the
Galactic dark matter mass profile on the one hand and on cosmic-ray propagation
on the other hand, we point out that considering a thermal annihilation cross
section for such low mass candidates very likely results in an antiproton flux
in tension with the current data, which should be taken into account in
subsequent studies.
