Background Infantile hypertrophic pyloric stenosis (IHPS) leads to excessive vomiting and metabolic alkalosis, which may subsequently cause apnea. Although it is generally assumed that metabolic derangements should be corrected prior to surgery to prevent apnea, the exact incidence of perioperative apneas in infants with IHPS and the association with metabolic alkalosis are unknown. We performed this systematic review to assess the incidence of apnea in infants with IHPS and to verify the possible association between apnea and metabolic alkalosis. Methods We searched MEDLINE, Embase, and Cochrane library to identify studies regarding infants with metabolic alkalosis, respiratory problems, and hypertrophic pyloric stenosis. We conducted a descriptive synthesis of the findings of the included studies. Results Thirteen studies were included for analysis. Six studies described preoperative apnea, three studies described postoperative apnea, and four studies described both. All studies were of low quality or had other research questions. We found an incidence of 27% of preoperative and 0.2%‐16% of postoperative apnea, respectively. None of the studies examined the association between apnea and metabolic alkalosis in infants with IHPS. Conclusions Infants with IHPS may have a risk to develop perioperative apnea. However, the incidence rates should be interpreted with caution because of the low quality and quantity of the studies. Therefore, further studies are required to determine the incidence of perioperative apnea in infants with IHPS. The precise underlying mechanism of apnea in these infants is still unknown, and the role of metabolic alkalosis should be further evaluated.