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The vacuum expectation value of the surface energy-momentum tensor of a charged scalar field is investigated for two parallel branes in anti-de Sitter spacetime with a compact spatial dimension. The existence of a constant gauge field is assumed, which leads to an Aharonov-Bohm type effect because of the nontrivial topology of the considered space. The contribution due to the presence of the hidden brane is extracted from the vacuum expectation value, and it is shown to be a cosmological constant type energy density on the visible brane. This cosmological constant is a periodic function of the magnetic flux through the compact dimension and, depending on the parameters of the problem, can be either positive or negative. For interbrane distances solving the hierarchy problem between the Planck and electroweak energy scales, the cosmological constant on the visible brane is naturally suppressed.