Anticipation of surgical procedures has been noted to be a major cause of anxiety, particularly in children and their parents. Preoperative anxiety in children is associated with complications before, during, and after surgery. There is therefore the need to identify predictors of preoperative anxiety in children, for early identification and development of interventions. This study aimed at determining predictors of preoperative anxiety in children. A total of 70 children with their parents, scheduled for general pediatric surgery in two teaching hospitals in Ghana, were recruited using a convenience sampling technique. Parental anxiety, perception of quality of healthcare, and preoperative anxiety in children were measured using the State Section of the State Trait Anxiety Inventory, the Pediatric Quality of Life—Healthcare Satisfaction Module, and the modified Yale Preoperative Anxiety Scale, respectively. Previous surgical experience, age and type of surgery were obtained by demographic questionnaire and hospital records. Majority of children who participated in the study were between ages 2 and 7 years (82.9%). 84.3% of parents in the study were females. Parental anxiety (β = 0.953, pp = 0.000) and perceived quality of healthcare (β = −0.257, p = 0.031) predicted preoperative anxiety in children. Older children scheduled for major surgery were more anxious in the preoperative period than younger children scheduled for major surgery (F = 6.75, p = 0.012). Comprehensive anxiety-alleviation protocols for pediatric surgery should involve parents as well as improving perceptions of quality of healthcare.