Recent X-ray polarimetric data on the prototypical black hole X-ray binary Cyg X-1 from the Imaging X-ray Polarimetry Explorer present tight constraints on accretion geometry in the hard spectral state. Contrary to general expectations of a low, less than or similar to 1% polarization degree (PD), the observed average PD was found to be a factor of 4 higher. Aligned with the jet position angle on the sky, the observed polarization favors geometry of the X-ray emission region stretched normally to the jet in the accretion disk plane. The high PD is, however, difficult to reconcile with the low orbital inclination of the binary i approximate to 30 degrees. We suggest that this puzzle can be explained if the emitting plasma is outflowing with a mildly relativistic velocity greater than or similar to 0.4 c. Our radiative transfer simulations show that Comptonization in the outflowing medium elongated in the plane of the disk and radiates X-rays with the degree and direction of polarization consistent with observations at i approximate to 30 degrees.