  The production of muons from heavy-flavour hadron decays in p-Pb collisions
at $\sqrt{{\textit s}_{\rm NN}}=5.02$ TeV was studied for $2 < p_{\rm T} < 16$
GeV/$c$ with the ALICE detector at the CERN LHC. The measurement was performed
at forward (p-going direction) and backward (Pb-going direction) rapidity, in
the ranges of rapidity in the center-of-mass system (cms) $2.03<y_{\rm
cms}<3.53$ and $-4.46<y_{\rm cms}<-2.96$, respectively. The production cross
sections and nuclear modification factors are presented as a function of
transverse momentum ($p_{\rm T}$). At forward rapidity, the nuclear
modification factor is compatible with unity while at backward rapidity, in the
interval $2.5<p_{\rm T}<3.5$ GeV/$c$, it is above unity by more than 2$\sigma$.
The ratio of the forward-to-backward production cross sections is also measured
in the overlapping interval $2.96 < \vert y_{\rm cms} \vert < 3.53$ and is
smaller than unity by 3.7$\sigma$ in $2.5<p_{\rm T}<3.5$ GeV/$c$. The data are
described by model calculations including cold nuclear matter effects.
