Dogs are one of the key animal species in investigating the biological mechanisms of behavioral laterality. Cerebral asymmetries are assumed to be influenced by stress, but this subject has not yet been studied in dogs. This study aims to investigate the effect of stress on laterality in dogs by using two different motor laterality tests: the Kong™ Test and a Food-Reaching Test (FRT). Motor laterality of chronically stressed (n = 28) and emotionally/physically healthy dogs (n = 32) were determined in two different environments, i.e., a home environment and a stressful open field test (OFT) environment. Physiological parameters including salivary cortisol, respiratory rate, and heart rate were measured for each dog, under both conditions. Cortisol results showed that acute stress induction by OFT was successful. A shift towards ambilaterality was detected in dogs after acute stress. Results also showed a significantly lower absolute laterality index in the chronically stressed dogs. Moreover, the direction of the first paw used in FRT was a good predictor of the general paw preference of an animal. Overall, these results provide evidence that both acute and chronic stress exposure can change behavioral asymmetries in dogs.