The elliptic flow, v2, of muons from heavy-flavour hadron decays at forward rapidity (2.5<y<4) is measured in Pb–Pb collisions at 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 v2 of muons from heavy-flavour hadron decays on the collision centrality, in the range 0–40%, and on transverse momentum, fadf95" title="Click to view the MathML source">pT, is studied in the interval 3<pT<10 GeV/c. A positive v2 is observed with the scalar product and two-particle Q cumulants in semi-central collisions (10–20% and 20–40% centrality classes) for the fadf95" title="Click to view the MathML source">pT interval from 3 to about 5 GeV/c with a significance larger than 3σ , based on the combination of statistical and systematic uncertainties. The v2 magnitude tends to decrease towards more central collisions and with increasing fadf95" title="Click to view the MathML source">pT. It becomes compatible with zero in the interval 6<pT<10 GeV/c. 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.