Crambe is an oilseed plant whose oil is suitable for various industrial purposes, such as production of biodiesel, plastics, rubbers, and cosmetics. There are reports of the rusticity of this species and its potential for growth in arid and semi-arid environments, where water scarcity and soil salinity are common. However, studies regarding the tolerance of its seeds to these stresses and the physiological responses triggered during germination and seedling establishment under these conditions are incipient. The objective of this study was to evaluate the tolerance of crambe seeds to water deficit and salt stress during germination and early seedling development, as well as to investigate the role of antioxidant enzymes on tolerance to these conditions. The seeds were exposed to water and salt stresses and their performance was analyzed. Seed water content, imbibition rate, percentage and speed of germination, and the base water potential for seed germination were evaluated. In the seedlings, the following measurements were made: root and shoot length, fresh and dry matter of roots and shoots, moisture content, and activity of the enzymes superoxide dismutase (SOD), catalase (CAT), and peroxidase (POX). Water deficit and salt stress reduce the water uptake rate of the seeds, the germination and growth of seedlings. The crambe seeds had higher tolerance to salt stress than to water deficit. Absorption of salt and the action of the SOD and CAT antioxidant enzymes are part of the tolerance mechanisms of crambe seeds to salt stress.