In everyday life we frequently rely on our abilities to postpone intentions until later occasions (prospective memory; PM) and to deactivate completed intentions even in stressful situations. Yet, little is known about the effects of acute stress on these abilities. In the present work we investigated the impact of acute stress on PM functioning under high task demands. (1) Different from previous studies, in which intention deactivation required mostly low processing demands, we used salient focal PM cues to induce high processing demands during intention-deactivation phases. (2) We systematically manipulated PM-monitoring demands in a nonfocal PM task that required participants to monitor for either one or six specific syllables that could occur in ongoing-task words. Eighty participants underwent the Trier Social Stress Test, a standardized stress induction protocol, or a standardized control situation, before performing a computerized PM task. Our primary interests were whether PM performance, PM-monitoring costs, aftereffects of completed intentions and/or commission-error risk would differ between stressed and non-stressed individuals and whether these effects would differ under varying task demands. Results revealed that PM performance and aftereffects of completed intentions during subsequent performance were not affected by acute stress induction, replicating previous findings. Under high demands on intention deactivation (focal condition), however, acute stress produced a nominal increase in erroneous PM responses after intention completion (commission errors). Most importantly, under high demands on PM monitoring (nonfocal condition), acute stress led to a substantial reduction in PM-monitoring costs. These findings support ideas of selective and demand-dependent effects of acute stress on cognitive functioning. Under high task demands, acute stress might induce a shift in processing strategy towards resource-saving behavior, which seems to increase the efficiency of PM performance (reduced monitoring costs), but might increase initial susceptibility to automatic response activation after intention completion.