Mars is seen as a basalt covered world that has been extensively altered through hydrothermal or near surface water-rock interactions. As a result, all the Fe/Mg-rich clay minerals detected from orbit so far have been interpreted as secondary, i.e. as products of aqueous alteration of pre-existing silicates by (sub)surface water. Based on the fine scale petrographic study of the evolved mesostasis of the Nakhla meteorite, we report here the presence of primary Fe/Mg-rich clay minerals that directly precipitated from a water-rich fluid exsolved from the Cl-rich parental melt of nakhlites during igneous differentiation. Such a tardi-magmatic precipitation of clay minerals requires much lower amounts of water compared to production via aqueous alteration. Although primary Fe/Mg-rich clay minerals are minor phases in Nakhla, the contribution of such a process to Martian clay formation may have been quite significant during the Noachian given that Noachian magmas were richer in H2O. In any case, the present discovery justifies a re-evaluation of the exact origin of the clay minerals detected on Mars so far, with potential consequences for our vision of the early magmatic and climatic histories of Mars.