A classical wave-optics analog of topological Aharonov-Bohm suppression of tunneling in a double-well potential on a ring threaded by a magnetic flux is proposed. The optical system consists of a uniformly twisted optical fiber with a structured annular core, in which the fiber twist mimics the role of the magnetic flux in the corresponding quantum-mechanical problem. Light waves trapped in the annular core of the fiber experience an additional topological Aharonov-Bohm phase, which may lead to the destruction of optical tunneling at certain values of the twist rate.