The effects of climate change on traditional stone fruit producing areas, together with the generation of new varieties with lower chilling requirements that allow the cultivation of previously unexplored areas, are setting up a challenging scenario for the establishment of productive orchards that must be more efficient in their capacity to adapt to new edaphoclimatic conditions. In this context, the rootstock breeding programs are a key piece in the agronomic strategy to achieve this adaptation through the development of rootstocks compatible with the new varieties and capable of transferring their tolerance to stress. An effective categorization of phenotypes within the germplasm involved in a plant breeding program is of utmost importance. Through the measurement of physiological parameters in both roots and leaves, tolerance to saline stress (120 mM NaCl) was evaluated in seven Prunus rootstocks whose genetic background included representatives of the subgenera Prunus, Cerasus, and Amygdalus. To group the genotypes according to their physiological performance under salt stress, an agglomerative hierarchical clustering was applied. The genotypes were grouped into three clusters containing rootstocks very sensitive (‘Mazzard F12/1’), moderately tolerant (‘Maxma 60’, ‘Cab6P’ and ‘AGAF 0204-09’), and tolerant (‘Mariana 2624’, ‘Garnem’ and ‘Colt’) to salt stress. ‘Mariana 2624’, a plum-based rootstock, was identified as the most tolerant Prunus rootstock. The information reported is valuable both in the productive context, for the selection of the most appropriate rootstocks to establish an orchard, and in the context of plant breeding programs, when choosing parents with outstanding traits to obtain progenies tolerant to salt stress.