  The imaginary part of the heavy quark-antiquark potential experienced by
moving heavy quarkonia in strongly coupled plasmas dual to theories of gravity
is computed by considering thermal worldsheet fluctuations of the holographic
Nambu-Goto string. General results for a wide class of gravity duals are
presented and an explicit formula for $\mathrm{Im} \, V_{Q\bar{Q}}$ is found in
the case where the axis of the moving $\bar{Q}Q$ pair has an arbitrary
orientation with respect to its velocity in the plasma. These results are
applied to the study of heavy quarkonia propagating through a strongly coupled
$\mathcal{N} = 4$ SYM plasma. Our results indicate that the onset of
$\mathrm{Im} \, V_{Q\bar{Q}}$ decreases with increasing rapidity (though our
analysis is limited to slowly moving quarkonia) and that, in general, a
$Q\bar{Q}$ pair is more strongly bound if its axis is aligned with its
direction of motion through the strongly coupled plasma.
