The momentum and spin of charge carriers in the topological insulators are constrained to be perpendicular to each other due to the strong spin-orbit coupling. We have investigated this unique spin-momentum locking property in Sb2Te3 topological insulator nanowires by injecting spin-polarized electrons through magnetic tunnel junction electrodes. Non-local voltage measurements exhibit a symmetry with respect to the magnetic field applied perpendicular to the nanowire channel, which is remarkably different from that of a non-local measurement in a channel that lacks spin-momentum locking. In stark contrast to conventional non-local spin valves, simultaneous reversal of magnetic moments of all magnetic contacts to the Sb2Te3 nanowire alters the non-local voltage. This unusual symmetry is a clear signature of the spin-momentum locking in the Sb2Te3 nanowire surface states.