The aim of the study was to verify the hypothesis regarding the effect of recommended (6.5 mg/kg) or enhanced (13 mg/kg) level of CuNPs in the diet in combination with different types of dietary fibre—cellulose (control), inulin, pectin or psyllium—on selected biological parameters of intestinal integrity in rats. Rats were randomly divided into 10 groups. The first two groups were fed a control diet that contained cellulose, and a mineral mixture with standard or enhanced content of CuCO3. Experimental groups were fed a diet supplemented with CuNPs (6.5 or 13 mg/kg) and combined with different types of fibre (cellulose, pectin, inulin or psyllium). After the feeding period, blood and small intestine samples were collected for further analysis. Replacing CuCO3 by CuNPs in the diet positively reduced the level of lactic acid and apoptosis markers in the small intestine; however, it also resulted in the intensification of DNA oxidation. The most beneficial effect on DNA repair mechanisms is related to inulin, while pectin has the greatest ability to inhibit inflammatory processes that induce the apoptotic death of cells in the small intestine. Our results suggest that dietary fibre supplementation protects the small intestine against potentially harmful, oxidative effects of CuNPs by intensifying the intestinal barrier.