The elliptic flow of electrons from beauty hadron decays at midrapidity (|y|<0.8) is measured in Pb-Pb collisions at sqrt[s_{NN}]=5.02 TeV with the ALICE detector at the LHC. The azimuthal distribution of the particles produced in the collisions can be parametrized with a Fourier expansion, in which the second harmonic coefficient represents the elliptic flow, v_{2}. The v_{2} coefficient of electrons from beauty hadron decays is measured for the first time in the transverse momentum (p_{T}) range 1.3-6 GeV/c in the centrality class 30%-50%. The measurement of electrons from beauty-hadron decays exploits their larger mean proper decay length cτ≈500 μm compared to that of charm hadrons and most of the other background sources. The v_{2} of electrons from beauty hadron decays at midrapidity is found to be positive with a significance of 3.75 σ. The results provide insights into the degree of thermalization of beauty quarks in the medium. A model assuming full thermalization of beauty quarks is strongly disfavored by the measurement at high p_{T}, but is in agreement with the results at low p_{T}. Transport models including substantial interactions of beauty quarks with an expanding strongly interacting medium describe the measurement within uncertainties.