  We study the effects of ultralight vector field (ULVF) dark matter on
gravitational wave propagation. We find that the coherent oscillations of the
vector field induce an anisotropic suppression of the gravitational wave
amplitude as compared to the $\Lambda$CDM prediction. The effect is enhanced
for smaller vector field masses and peaks for modes around
$k=H_0/\sqrt{a(H=m)}$. The suppression is negligible for astrophysically
generated gravitational waves but could be sizeable for primordial gravity
waves. We discuss the possibility of detecting such an effect on the CMB B-mode
power spectrum with the sensitivity of future detectors. We find that the
upcoming LiteBIRD mission would be sensitive to ULVF dark matter with masses
$m\lesssim 10^{-26}$ eV for sufficiently large abundances.
