The date palm, a central plant in the fragile oasis ecosystem, is considered one of the fruit species most tolerant to salt stress. However, the tolerance mechanisms involved are yet to be addressed and their evaluation until now was mainly based on heterogenous plant material such as seedlings or limited to in vitro experiment conditions. For these reasons, we propose to deepen our knowledge of the morphological and physiological responses to salt stress using acclimated ex vitro plants resulting from the propagation of a single genotype. The plants were irrigated with 0, 150, 300, or 450 mM NaCl solutions for four months. Our results showed that the influence of water salinity on growth and ion-homeostasis regulation was very dependent on stress levels. The 150 mM NaCl concentration was found to improve dry biomass by about 35%, but at higher salt concentrations (300 and 450 mM) it decreased by 40–65%. The shoot:root dry mass ratio decreased significantly at the 150 mM NaCl water concentration and then increased with increasing water salt concentration. The leaf:root ratio for Na+ and Cl− decreased significantly with increasing water salinity up to a concentration of 300 mM NaCl, and then stabilized with similar values for 300 mM and 450 mM NaCl. In contrast to Na+ and Cl−, leaf K+ content was significantly higher in the leaf than in the root for all salt treatments. Unlike Na+ and K+, Cl− was expelled to the surface of leaves in response to increased water salinity. Overall, date palm plants appear to be more capable of excluding Cl− than Na+ and of changing biomass allocation according to salt-stress level, and their leaves and roots both appear to play an important role in this tolerance strategy.