Post-prandial hyperglycemia typical of diabetes mellitus could be alleviated using plant-derived compounds such as polyphenols, which could influence the activities of enzymes involved in carbohydrate digestion and of intestinal glucose transporters. Here, we report on the potential anti-hyperglycemic effect of Crocus sativus tepals compared to stigmas, within the framework of valorizing these by-products of the saffron industry, since the anti-diabetic properties of saffron are well-known, but not those of its tepals. In vitro assays showed that tepal extracts (TE) had a greater inhibitory action than stigma extracts (SE) on α-amylase activity (IC50: TE = 0.60 ± 0.09 mg/mL; SE = 1.10 ± 0.08 mg/mL; acarbose = 0.051 ± 0.07) and on glucose absorption in Caco-2 differentiated cells (TE = 1.20 ± 0.02 mg/mL; SE = 2.30 ± 0.02 mg/mL; phlorizin = 0.23 ± 0.01). Virtual screening performed with principal compounds from stigma and tepals of C. sativus and human pancreatic α-amylase, glucose transporter 2 (GLUT2) and sodium glucose co-transporter-1 (SGLT1) were validated via molecular docking, e.g., for human pancreatic α-amylase, epicatechin 3-o-gallate and catechin-3-o-gallate were the best scored ligands from tepals (−9.5 kcal/mol and −9.4 kcal/mol, respectively), while sesamin and episesamin were the best scored ones from stigmas (−10.1 kcal/mol). Overall, the results point to the potential of C. sativus tepal extracts in the prevention/management of diabetes, likely due to the rich pool of phytocompounds characterized using high-resolution mass spectrometry, some of which are capable of binding and interacting with proteins involved in starch digestion and intestinal glucose transport.