  Renormalization factors for three- and four-quark operators, which appear in
the low energy effective Lagrangian of the proton decay and the weak
interactions, are perturbatively calculated in domain-wall QCD. We find that
the operators are multiplicatively renormalizable up to one-loop level without
mixing with any other operators that have different chiral structures. As an
application, we evaluate a renormalization factor for $B_K$ at the parameters
where previous simulations have been performed, and find one-loop corrections
to $B_K$ are 1-5% in these cases.
