Grape pomace (GP) is a winemaking by-product rich in polyphenols and fibre. Supplementation with GP extracts has shown potential benefits against oxidative stress- and inflammation-related pathologies. As a new nutritional target, this paper explores the impact of the ingestion of a grape pomace extract on intestinal barrier functionality. A GP extract was sequentially subjected to gastrointestinal and colonic digestion using the dynamic gastrointestinal simulator (simgi®). This generated two simulated fluids: intestinal-digested extract (IDE) and colonic-digested extract (CDE). The effects of these two fluids on paracellular permeability and the expression of tight junction (TJ) proteins (i.e., zonula occludens-1 (ZO-1) and occludin) were assessed in Caco-2-cell monolayers grown in Transwell® inserts. The IDE fluid significantly (p < 0.001) reduced the paracellular transport of FITC-dextran with respect to the control, whereas no significant differences (p > 0.05) were found for CDE, which could be due, at least partially, to the pro-leaky effect of the colonic digestion medium. Accordant slight increases in the mRNA levels of both ZO-1 and occludin were observed for IDE, but without statistical significance. Additionally, the colonic fermentation of the GP extract promoted the production of short-chain fatty acids (SCFA) and phenolic metabolites and led to changes in the relative abundance of some bacteria that might affect paracellular permeability. Overall, this paper reports first trends about the effects of grape pomace extracts on intestinal permeability that would require further confirmation in future experiments.