In the context of brane-world extra-dimensional theories, we compute the positron production from branon dark matter annihilations and compare with the AMS-02 data. Three different scenarios have been considered; the first two assume that either pulsars or dark matter may explain separately the whole positron fraction as measured by AMS-02, whereas the third one assumes that a suitable combination of these two contributions is needed. For all of them, exclusion diagrams for the brane mass and the tension of the brane, were obtained. Our analysis has been performed for a minimal, a medium and a maximum diffusion model in one extra dimension for both pseudo-Isothermal and Navarro-Frenk-White dark matter halos. Combined with previous cosmological analyses and experimental data in colliders, constraints here enable us to set further bounds on the parameter space of branons. In particular, in the case when pulsars fit the whole AMS-02 data, we have excluded mass-tension regions for masses and tensions smaller than 60.75 TeV and 8.56 TeV respectively. With regard to the scenario in which AMS-02 data are explained by a combination of dark matter and pulsars, masses and tensions smaller than 27.32 TeV and 3.85 TeV respectively turn out to be excluded. Finally, in the scenario with no pulsar contribution, a branon with a mass 38.1 ± 0.2 TeV and a tension 4.99 ± 0.04 TeV can fit well the experimental data.