The polarization of inclusive J/ψ and ϒ(1S) produced in Pb–Pb collisions at s_NN=5.02 TeV at the LHC is measured with the ALICE detector. The study is carried out by reconstructing the quarkonium through its decay to muon pairs in the rapidity region 2.5<y<4 and measuring the polar and azimuthal angular distributions of the muons. The polarization parameters λ_θ, λ_ϕ and λ_θϕ are measured in the helicity and Collins-Soper reference frames, in the transverse momentum interval 2<p_T<10 GeV/c and p_T<15 GeV/c for the J/ψ and ϒ(1S), respectively. The polarization parameters for the J/ψ are found to be compatible with zero, within a maximum of about two standard deviations at low p_T, for both reference frames and over the whole p_T range. The values are compared with the corresponding results obtained for pp collisions at s=7 and 8 TeV in a similar kinematic region by the ALICE and LHCb experiments. Although with much larger uncertainties, the polarization parameters for ϒ(1S) production in Pb–Pb collisions are also consistent with zero.