We consider measurements of exclusive rare semi-tauonic b-hadron decays, mediated by the b → sτ + τ − transition, at a future high-energy circular electron-positron collider (FCC-ee). We argue that the high boosts of b-hadrons originating from on-shell Z boson decays allow for a full reconstruction of the decay kinematics in hadronic τ decay modes (up to discrete ambiguities). This, together with the potentially large statistics of Z → bb, opens the door for the experimental determination of τ polarizations in these rare b-hadron decays. In the light of the current experimental situation on lepton flavor universality in rare semileptonic B decays, we discuss the complementary short-distance physics information carried by the τ polarizations and suggest suitable theoretically clean observables in the form of single-and double-τ polarization asymmetries.