The relative velocity between baryons and dark matter in the early Universe can suppress the formation of small-scale baryonic structure and leave an imprint on the baryon acoustic oscillation (BAO) scale at low redshifts after reionization. This streaming velocity affects the post-reionization gas distribution by directly reducing the abundance of pre-existing mini-halos ($lesssim 10^7 M_{bigodot}$) that could be destroyed by reionization and indirectly modulating reionization history via photoionization within these mini-halos. In this work, we investigate the effect of streaming velocity on the BAO feature in HI 21 cm intensity mapping after reionization, with a focus on redshifts $3.5lesssim zlesssim5.5$. We build a spatially modulated halo model that includes the dependence of the filtering mass on the local reionization redshift and thermal history of the intergalactic gas. In our fiducial model, we find isotropic streaming velocity bias coefficients $b_v$ ranging from $-0.0033$ at $z=3.5$ to $-0.0248$ at $z=5.5$, which indicates that the BAO scale is stretched (i.e., the peaks shift to lower $k$). In particular, streaming velocity shifts the transverse BAO scale between 0.087% ($z=3.5$) and 0.37% ($z=5.5$) and shifts the radial BAO scale between 0.13% ($z=3.5$) and 0.52% ($z=5.5$). These shifts exceed the projected error bars from the more ambitious proposed hemispherical-scale surveys in HI (0.13% at $1sigma$ per $Delta z = 0.5$ bin).
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