Complementarity in phosphorus (P) acquisition from different sources and facilitation of P uptake have been implicated in yield advantages of intercropping. These beneficial interactions between crop species are expected to be particularly relevant on low-P soils. Millet and chickpea have previously been found to differ in their ability to access different chemically bound forms of P. Here, we conducted a two-year field experiment on a low-P soil with or without P fertilization to determine whether the resulting potential for complementarity and facilitation with respect to P acquisition is associated with increased P uptake and yield of an intercrop as compared to sole crops. Alkaline phosphatase activity and carboxylate concentration differed between millet and chickpea, indicating potential complementarity in access to different P sources. Comparison of aboveground P content in the intercrop and the pure stands showed a positive net effect for P uptake (NEP > 0) when no P fertilizer was applied, but this positive net effect for P acquisition was not associated with a yield increase (NEY = 0). When P fertilizer was applied, there was no significant net increase in P uptake by the intercrop compared to sole crops (NEP = 0), but there was a significant yield gain (NEY > 0). Species trait dissimilarities for P acquisition from different sources supported complementarity in, and facilitation of P uptake by millet and chickpea in the field on a low-P soil, but this did not result in yield increase. The finding does not support the notion that complementarity in P acquisition from different sources and facilitation of P uptake are key drivers for overyielding by intercropping on low-P soil.