Background: Clinically relevant acute postoperative pancreatitis (CR-PPAP) after pancreaticoduodenectomy (PD) is a complication that may lead to the development of local and systemic consequences. The study aimed to identify risk factors for CR-PPAP and assess the impact of CR-PPAP on the postoperative course after PD. Methods: The study retrospectively analyzed data from 428 consecutive patients who underwent PD at a single center between January 2013 and December 2022. The presence of increased amylase activity in plasma, above the upper limit of normal 48 h after surgery, was checked. CR-PPAP was diagnosed when accompanied by disturbing radiological features and/or symptoms requiring treatment. We investigated the relationship between the occurrence of CR-PPAP and the development of postoperative complications after PD, and possible predictors of CR-PPAP. Results: The postoperative follow-up period was 90 days. Of the 428 patients, 18.2% (n = 78) had CR-PPAP. It was associated with increased rates of CR-POPF, delayed gastric emptying, occurrence of intra-abdominal collections, postoperative hemorrhage, peritonitis, and septic shock. Patients who developed CR-PPAP were more often reoperated (37.17% vs. 6.9%, p < 0.0001)) and had increased postoperative mortality (14.1% vs. 5.74%, p < 0.0001). Soft pancreatic parenchyma, intraoperative blood loss, small diameter of the pancreatic duct, and diagnosis of adenocarcinoma papillae Vateri were independent risk factors for CR-PPAP and showed the best performance in predicting CR-PPAP. Conclusions: CR-PPAP is associated with an increased incidence of postoperative complications after PD, worse treatment outcomes, and an increased risk of reoperation and mortality. Pancreatic consistency, intraoperative blood loss, width of the duct of Wirsung, and histopathological diagnosis can be used to assess the risk of CR-PPAP. Amylase activity 48 h after surgery > 161 U/L is highly specific in the diagnosis of CR-PPAP.