We investigate the effect of supersonic relative velocities between baryons and dark matter, recently shown to arise generically at high redshift, on baryonic acoustic oscillation (BAO) measurements at low redshift. The amplitude of the relative velocity effect at low redshift is model-dependent, but can be parameterized by using an unknown bias. We find that if unaccounted, the relative velocity effect can shift the BAO peak position and bias estimates of the dark energy equation-of-state due to its non-smooth, out-of-phase oscillation structure around the BAO scale. Fortunately, the relative velocity effect can be easily modeled in constraining cosmological parameters without substantially inflating the error budget. We also demonstrate that the presence of the relative velocity effect gives rise to a unique signature in the galaxy bispectrum, which can be utilized to isolate this effect. Future dark energy surveys can accurately measure the relative velocity effect and subtract it from the power spectrum analysis to constrain dark energy models with high precision.