[en] The polarization of inclusive $\mathrm{J}/\psi$ and $\mathrm{\Upsilon }(1\mathrm{S})$ produced in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ 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 ${\lambda }_{\theta }$, ${\lambda }_{\varphi }$ and ${\lambda }_{\theta \varphi }$ are measured in the helicity and Collins-Soper reference frames, in the transverse momentum interval $2<p_{\mathrm{T}}<10$ GeV/c and $p_{\mathrm{T}}<15$ GeV/c for the $\mathrm{J}/\psi$ and $\mathrm{\Upsilon }(1\mathrm{S})$, respectively. The polarization parameters for the $\mathrm{J}/\psi$ are found to be compatible with zero, within a maximum of about two standard deviations at low $p_{\mathrm{T}}$, for both reference frames and over the whole $p_{\mathrm{T}}$ range. The values are compared with the corresponding results obtained for pp collisions at $\sqrt{s}=7$ and 8 TeV in a similar kinematic region by the ALICE and LHCb experiments. Although with much larger uncertainties, the polarization parameters for $\mathrm{\Upsilon }(1\mathrm{S})$ production in Pb–Pb collisions are also consistent with zero.