Wild progenitors of common wheat are a potential source of tolerance to biotic and abiotic stresses. We conducted a glasshouse pot experiment to study genotypic differences in response to drought stress in a collection of 180 accessions of Aegilops and Triticum along with one tolerant and one sensitive control variety. Several physiological traits and chlorophyll fluorescence parameters were evaluated. Our findings indicated that drought significantly reduced shoot fresh (59.45%) and dry (50.83%) weights, stomatal conductance (41.52%) and maximum photosynthetic capacity (41.06%), but increased initial fluorescence (28.10%). Drought stress also decreased the chlorophyll content, relative water content and maximum quantum efficiency by 14.90, 12.13 and 11.42%, respectively. Principal component analysis of the 182 individuals identified three components that explained 57.61 and 61.68% of the total variation in physiological and photosynthetic traits under control and stress conditions, respectively. When grouped into the 12 species tested, the three top components explained 78.22% of the total variation under drought. The means comparison, stress tolerance index and biplot analysis identified five accessions with superior tolerance to drought. Remarkably, four species of wild relatives—Ae. cylindrica (DC genome), Ae. crassa (DM genome), Ae. caudata (C genome) and T. urartu (Au genome)—responded well to drought stress with a lower percentage decline for most traits and high values for the first two components. The potential of these species offers further opportunities for analysis at the molecular and cellular levels to confront with drought stress through a physiological mechanism.