Social stress affects cognitive processes in general, and memory performance in particular. However, the direction of these effects has not been clearly established, as it depends on several factors. Our aim was to determine the impact of the hypothalamus-pituitary-adrenal (HPA) axis and sympathetic nervous system (SNS) reactivity to psychosocial stress on short-term non-declarative memory and declarative memory performance. Fifty-two young participants (18 men, 34 women) were subjected to the Trier Social Stress Task (TSST) and a control condition in a crossover design. Implicit memory was assessed by a priming test, and explicit memory was assessed by the Rey Auditory Verbal Learning Test (RAVLT). The TSST provoked greater salivary cortisol and salivary alpha-amylase (sAA) responses than the control task. Men had a higher cortisol response to stress than women, but no sex differences were found for sAA release. Stress was associated with an enhancement of priming but did not affect declarative memory. Additionally, the enhancement on the priming test was higher in those whose sAA levels increased more in response to stress (r(48) = 0.339, p = 0.018). Our results confirm an effect of acute stress on priming, and that this effect is related to SNS activity. In addition, they suggest a different relationship between stress biomarkers and the different memory systems.