We propose to utilize the exclusive Z-boson rare decays Z→ϒ(ns)+γ to constrain the Zbb¯ couplings at the HL-LHC and 100 TeV proton-proton collider. We demonstrate that the event yield of the proposed processes is sensitive to the axial-vector component of the Zbb¯ coupling and can provide complementary information to the jet-charge weighted single-spin asymmetry measurement at the EIC and the gg→Zh production rate measurement at the LHC. By applying the NRQCD factorization formalism, we calculate the partial decay width of Z→ϒ(ns)+γ to the NLO accuracy in strong interaction, which is found to agree with those obtained from the light-cone distribution amplitude approach. We show that the HL-LHC can break the degeneracy of the Zbb¯ couplings, as implied by the precision electroweak data at LEP and SLC, if the signal efficiency can be improved by a factor of 1.7 from the present ATLAS analysis at the 13 TeV LHC with an integrated luminosity of 36.1fb−1.