51 pages, 25 figures.We analyse the phenomenology of orbifold scenarios from the heterotic superstring, and the resulting theoretical predictions for the direct detection of neutralino dark matter. In particular, we study the parameter space of these constructions, computing the low-energy spectrum and taking into account the most recent experimental and astrophysical constraints, as well as imposing the absence of dangerous charge and colour breaking minima. In the remaining allowed regions the spin-independent part of the neutralino-proton cross section is calculated and compared with the sensitivity of dark matter detectors. In addition to the usual non universalities of the soft terms in orbifold scenarios due to the modular weight dependence, we also consider D-term contributions to scalar masses. These are generated by the presence of an anomalous U(1), providing more flexibility in the resulting soft terms, and are crucial in order to avoid charge and colour breaking minima. Thanks to the D-term contribution, large neutralino detection cross sections can be found, within the reach of projected dark matter detectors.D.G. Cerdeño is supported by the program "Juan de la Cierva" of the Ministerio de Educación y Ciencia of Spain. T. Kobayashi is supported in part by the Grand-in-Aid for Scientific Research #17540251 and the Grant-in-Aid for the 21st Century COE "The Center for Diversity and Universality in Physics" from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The work of C. Muñoz was supported in part by the Spanish DGI of the MEC under Proyecto Nacional FPA2006- 05423, by the European Union under the RTN program MRTN-CT-2004-503369, and under the ENTApP Network of the ILIAS project RII3-CT-2004-506222. Likewise, the work of D. G. Cerdeño and C. Muñoz, was also supported in part by the Spanish DGI of the MEC under Proyecto Nacional FPA2006-01105, by the Comunidad de Madrid under Proyecto HEPHACOS, Ayudas de I+D S-0505/ESP-0346, and by the EU research and training network MRTN-CT-2006-035863.