Stress has been widely studied in different mammals, but the physiological stress reaction that the odour of a predator could induce in preys has not received much attention. Besides, not all the animals would respond to the same extent to a known stressor. We developed an experimental procedure with eleven naïve European rabbits (Oryctolagus cuniculus) in order to determine the individual physiological response to the olfactory detection of a potential predator. The rabbits were housed singly in small enclosures with a concrete burrow system and food and water were available ad libitum. The animals followed a control trial, without odour, and an experimental trial where we confronted the rabbits with fox (Vulpes vulpes) odour. Furthermore, another sample of eleven rabbits followed a control procedure subjected to the same housing and handling procedures but without facing the predator odour. In order to assess the physiological response we analysed the concentration of glucocorticoid metabolites in the faeces of the rabbits. Therefore, everyday faecal samples were collected and analysed with an enzyme immunoassay in order to measure the corticosterone metabolites (CM), particularly, those metabolites with a 5α-3β, 11β-diol structure. After validating the assay for wild rabbits, we found that the simulated presence of a predator (fox odour) in the enclosure resulted in an increase in faecal CM concentrations. However, the stressor did not affect all the animals in the same way. We found a general increase in the individual differences. In particular, males experienced a higher increase than females, though the overall response was similar for both sexes. To our knowledge this is one of the first attempts to analyse the assessment of the risk of predation by means of non-invasive methods.