The polarization of the Λ and Λ[over ¯] hyperons along the beam (z) direction, P_{z}, has been measured in Pb-Pb collisions at sqrt[s_{NN}]=5.02  TeV recorded with ALICE at the Large Hadron Collider (LHC). The main contribution to P_{z} comes from elliptic flow-induced vorticity and can be characterized by the second Fourier sine coefficient P_{z,s2}=⟨P_{z}sin(2φ-2Ψ_{2})⟩, where φ is the hyperon azimuthal emission angle and Ψ_{2} is the elliptic flow plane angle. We report the measurement of P_{z,s2} for different collision centralities and in the 30%-50% centrality interval as a function of the hyperon transverse momentum and rapidity. The P_{z,s2} is positive similarly as measured by the STAR Collaboration in Au-Au collisions at sqrt[s_{NN}]=200  GeV, with somewhat smaller amplitude in the semicentral collisions. This is the first experimental evidence of a nonzero hyperon P_{z} in Pb-Pb collisions at the LHC. The comparison of the measured P_{z,s2} with the hydrodynamic model calculations shows sensitivity to the competing contributions from thermal and the recently found shear-induced vorticity, as well as to whether the polarization is acquired at the quark-gluon plasma or the hadronic phase.