The production of Z⁰ bosons at large rapidities in Pb–Pb collisions at s_NN=5.02TeV is reported. Z⁰ candidates are reconstructed in the dimuon decay channel (Z⁰→μ⁺μ⁻), based on muons selected with pseudo-rapidity −4.0<η<−2.5 and p_T>20GeV/c. The invariant yield and the nuclear modification factor, R_AA, are presented as a function of rapidity and collision centrality. The value of R_AA for the 0–20% central Pb–Pb collisions is 0.67±0.11(stat.)±0.03(syst.)±0.06(corr. syst.), exhibiting a deviation of 2.6σ from unity. The results are well-described by calculations that include nuclear modifications of the parton distribution functions, while the predictions using vacuum PDFs deviate from data by 2.3σ in the 0–90% centrality class and by 3σ in the 0–20% central collisions.