The fraction of χ_{c1} and χ_{c2} decays in the prompt J/ψ yield, F_{χ_{c}→J/ψ}=σ_{χ_{c}→J/ψ}/σ_{J/ψ}, is measured by the LHCb detector in pPb collisions at sqrt[s_{NN}]=8.16 TeV. The study covers the forward (1.5<y^{*}<4.0) and backward (-5.0<y^{*}<-2.5) rapidity regions, where y^{*} is the J/ψ rapidity in the nucleon-nucleon center-of-mass system. Forward and backward rapidity samples correspond to integrated luminosities of 13.6±0.3 and 20.8±0.5 nb^{-1}, respectively. The result is presented as a function of the J/ψ transverse momentum p_{T,J/ψ} in the range 1<p_{T,J/ψ}<20 GeV/c. The F_{χ_{c}→J/ψ} fraction at forward rapidity is compatible with the LHCb measurement performed in pp collisions at sqrt[s]=7 TeV, whereas the result at backward rapidity is 2.4σ larger than in the forward region for 1<p_{T,J/ψ}<3 GeV/c. The increase of F_{χ_{c}→J/ψ} at low p_{T,J/ψ} at backward rapidity is compatible with the suppression of the ψ(2S) contribution to the prompt J/ψ yield. The lack of in-medium dissociation of χ_{c} states observed in this study sets an upper limit of 180 MeV on the free energy available in these pPb collisions to dissociate or inhibit charmonium state formation.