The first measurement of the $\Upsilon(1{\rm S})$ elliptic flow coefficient ($v_2$) is performed at forward
rapidity (2.5~$<$~{\it y}~$<$~4) in Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$~TeV with
the ALICE detector at the LHC. The results are obtained with the scalar product method and are
reported as a function of transverse momentum (\pt) up to 15 GeV/$c$ in the 5--60\% centrality interval. The measured $\Upsilon(1{\rm S})$ $v_2$ is consistent with zero
and with the small positive values predicted by transport models within uncertainties.
The $v_2$ coefficient in 2~$<$~$p_{\rm T}$~$<$~15 GeV/$c$ is lower than that of inclusive \jpsi~mesons in the same \pt{} interval by 2.6 standard deviations. These results, combined with earlier suppression measurements, are in agreement with a scenario in which the $\Upsilon$(1S) production in Pb--Pb collisions at LHC energies is dominated by dissociation limited to the early stage of the collision whereas in the J/$\psi$ case there is substantial experimental evidence of an additional regeneration component.