Pistacia atlantica Desf. is adapted to arid and semi-arid environments and is considered the best rootstock for Pistacia vera L. The physiological mechanisms responsible for the efficiency of P. atlantica as rootstock, compared to P. vera, are unknown. This study evaluated the effect of water stress and pistachio rootstock (Pistacia vera L. and Pistacia atlantica Desf.) on water status, highlighting the physiological aspects of the scion-rootstock interaction in Pistacia vera L. and Pistacia atlantica Desf. at the seedling stage under water stress. Individuals of Pistacia vera L. were grafted on Pistacia vera and Pistacia atlantica for 2 years, and subjected to two water regimes: irrigation and water stress for 7 weeks. Water status parameters (relative water content (RWC) and soil water content (SWC)), leaf gas exchange parameters (stomatal conductance, net photosynthesis, and transpiration rate), chlorophyll fluorescence transient (OJIP), maximum photosynthetic yield (Fv/Fm), and total chlorophyll content were measured weekly. The results revealed that although soil water content decreased significantly, both rootstocks maintained a high level of hydration, slightly reduced leaf gas exchange, and a stable maximum photosynthetic yield during the water stress, with no clear differences between them. These results suggest that Pistacia vera L. grafted on Pistacia vera L. and Pistacia atlantica Desf. tolerates water stress at the seedling stage in field conditions. These findings are very important in agriculture, and we recommend the investigation of drought stress effect at the tree stage and for a long duration of water stress.