Oat husk (hull) is a byproduct of oat processing that is rich in insoluble fiber. The aim of the study was to evaluate the effect of partially replacing wheat flour with oat husk (at levels of 0, 5, 10, 15, and 20 g/100 g) on the physicochemical properties and sensory acceptance of pasta. Additionally, UPLC-MS/MS analysis was performed to identify phenolic acids and flavonoid compounds, and the cooking properties of the pasta were evaluated. The test results indicate that oat husk significantly (p < 0.05) increased the ash and fiber contents in the pasta, while decreasing the protein and fat contents. Moreover, the redness and yellowness of both raw and cooked pasta increased, while lightness decreased as a result of pasta enrichment with oat husk. Oat husk also led to a decrease in the stretching force of cooked samples, although cooking loss increased significantly but did not exceed 8%. The contents of phenolics and antioxidant activity significantly increased with the incorporation of hull in pasta recipes. UPLC-MS/MS analysis showed that the enriched pasta was especially abundant in ferulic acid. Products with up to 10 g of husk/100 g of wheat flour showed good consumer acceptance. However, higher levels of this additive led to notably lower assessments, particularly in terms of pasta texture.