Intestinal transepithelial transport of glucose is mediated by glucose transporters, and affects postprandial blood-glucose levels. This study investigates the effect of wood extracts rich in hydrolyzable tannins (HTs) that originated from sweet chestnut (Castanea sativa Mill.) and oak (Quercus petraea) on the expression of glucose transporter genes and the uptake of glucose and HT constituents in a 3D porcine-small-intestine epithelial-cell model. The viability of epithelial cells CLAB and PSI exposed to different HTs was determined using alamarBlue®. qPCR was used to analyze the gene expression of SGLT1, GLUT2, GLUT4, and POLR2A. Glucose uptake was confirmed by assay, and LC–MS/ MS was used for the analysis of HT bioavailability. HTs at 37 µg/mL were found to adversely affect cell viability and downregulate POLR2A expression. HT from wood extract Tanex at concentrations of 4 µg/mL upregulated the expression of GLUT2, as well as glucose uptake at 1 µg/mL. The time-dependent passage of gallic acid through enterocytes was influenced by all wood extracts compared to gallic acid itself as a control. These results suggest that HTs could modulate glucose uptake and gallic acid passage in the 3D cell model.