The elliptic flow, v2tainer hidden">, of muons from heavy-flavour hadron decays at forward rapidity (2.5<y<4tainer hidden">) is measured in Pb–Pb collisions at tainer hidden"> with the ALICE detector at the LHC. The scalar product, two- and four-particle Q cumulants and Lee–Yang zeros methods are used. The dependence of the v2tainer hidden"> of muons from heavy-flavour hadron decays on the collision centrality, in the range 0–40%, and on transverse momentum, pTtainer hidden">, is studied in the interval 3<pT<10 GeV/ctainer hidden">. A positive v2tainer hidden"> is observed with the scalar product and two-particle Q cumulants in semi-central collisions (10–20% and 20–40% centrality classes) for the pTtainer hidden"> interval from 3 to about 5 GeV/ctainer hidden"> with a significance larger than 3σ , based on the combination of statistical and systematic uncertainties. The v2tainer hidden"> magnitude tends to decrease towards more central collisions and with increasing pTtainer hidden">. It becomes compatible with zero in the interval 6<pT<10 GeV/ctainer hidden">. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions.