  We show that QCD undergoes dimensional reduction at high temperatures also in
the quark sector. In the kinematic region relevant to screening physics, where
the lowest Matsubara modes are close to their ``mass-shells'', all static
Green's functions involving both quarks and gluons, are reproducible in the
high-$T$ limit by a renormalizable three dimensional Lagrangian up to order
$\tilde{g}^2(T)\sim 1/ln T$. This three dimensional theory only contains
explicitly the lightest bosonic and fermionic Matsubara modes, while the
heavier modes correct the tree-level couplings and generate extra local
vertices. We also find that the quark degrees of freedom that have been
retained in the reduced theory are nonrelativistic in the high-$T$ limit. We
then improve our result to order $\tilde{g}^4(T)$ through an explicit
nonrelativistic expansion, in the spirit of the heavy quark effective theory.
This effective theory is relevant for studying QCD screening phenomena with
observables made from quarks, e.g. mesonic and baryonic currents, already at
temperatures not much higher than the chiral transition temperature $T_c$.
