Many individuals perceived the COVID-19 pandemic as a profound traumatic occurrence that triggered substantial increases in fear, anxiety, and PTSD symptoms. While negative cognitive appraisals have long been linked to the emergence and continuation of emotional difficulties, considerably fewer studies have explored how positive, adaptive appraisals may help safeguard mental well-being. This research aimed to bridge that gap by examining the influence of problem-solving appraisals on the connection between fear of COVID-19 and PTSD symptoms. The sample consisted of 322 university students who completed the Fear of COVID-19 Scale, the Problem-Solving Inventory, the PTSD Checklist for DSM-5, and the five-item short form of the State–Trait Anxiety Inventory. The participants’ mean age was 26 years (± 10.2; range 17–63 years). Findings showed that problem-solving appraisal acted as a mediator between fear of COVID-19 and every dimension of PTSD. However, further analysis revealed that anxiety levels moderated this mediation. The indirect pathway from fear of COVID-19 to PTSD was statistically significant only among individuals reporting low anxiety. These results highlight the importance of interventions that identify and modify unhelpful views of one’s problem-solving capabilities while also tackling anxiety symptoms that can obstruct effective coping.