  Consider the time-periodic viscous incompressible fluid flow past a body with
non-zero velocity at infinity. This article gives sufficient conditions such
that weak solutions to this problem are smooth. Since time-periodic solutions
do not have finite kinetic energy in general, the well-known regularity results
for weak solutions to the corresponding initial-value problem cannot be
transferred directly. The established regularity criterion demands a certain
integrability of the purely periodic part of the velocity field or its
gradient, but it does not concern the time mean of these quantities.
