The elliptic flow, Support mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009156&_mathId=si2.gif&_user=111111111&_pii=S0370269315009156&_rdoc=1&_issn=03702693&md5=af612936c94892de2098a0b323cdcab5" title="Click to view the MathML source">v<sub>2sub>, 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 v<sub>2sub> of muons from heavy-flavour hadron decays on the collision centrality, in the range 0–40%, and on transverse momentum, p<sub>Tsub>, is studied in the interval 3<p<sub>Tsub><10 GeV/c. A positive v<sub>2sub> is observed with the scalar product and two-particle Q cumulants in semi-central collisions (10–20% and 20–40% centrality classes) for the p<sub>Tsub> interval from 3 to about 5 GeV/c with a significance larger than 3σ , based on the combination of statistical and systematic uncertainties. The v<sub>2sub> magnitude tends to decrease towards more central collisions and with increasing p<sub>Tsub>. It becomes compatible with zero in the interval 6<p<sub>Tsub><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.