Unwanted imaginations of future fears can, to some extent, be avoided. This is achieved by control mechanisms similar to those engaged to suppress and forget unwanted memories. Suppression-induced forgetting relies on the executive control network, whose functioning is impaired after exposure to acute stress. This study investigates whether acute stress affects the ability to intentionally control future fears and, furthermore, whether individual differences in executive control predict a susceptibility to these effects. The study ran over two consecutive days. On day 1, the working memory capacity of one hundred participants was assessed. Thereafter, participants provided descriptions and details of fearful episodes that they imagined might happen in their future. On day 2, participants were exposed to either the stress or no-stress version of the Maastricht Acute Stress Test, after which participants performed the Imagine/No-Imagine task. Here, participants repeatedly imagined some future fears and suppressed imaginings of others. Results demonstrated that, in unstressed participants, suppression successfully induced forgetting of the episodes' details compared to a baseline condition. However, anxiety toward these events did not differ. Acute stress was found to selectively impair suppression-induced forgetting and, further, this effect was moderated by working memory capacity. Specifically, lower working memory predicted a susceptibility to these detrimental effects. These findings provide novel insights into conditions under which our capacity to actively control future fears is reduced, which may have considerable implications for understanding stress-related psychopathologies and symptomatologies characterized by unwanted apprehensive thoughts.