Pasta production is a good opportunity for product innovation in different forms. The aim of this work was to assess the use of flaxseed components for pasta production. We examined the chemical composition and cooking quality, at different contents of flaxseed flour (FF) and flaxseed cake (FC), added for pasta processing. The analysis showed that the addition of flaxseed components to the dough caused a substantial difference in the International Commission on Illumination color model (CIE) parameter, compared to control samples. The samples of pasta with FF and FC were darker, redder, and less yellow than the control. The minimum cooking time for the enriched pasta was longer than that for the control pasta, although cooking losses were lower. The increasing content of flaxseed components did not significantly change the weight and volume increase index. The enrichment of pasta with 23% FF and 17% FC yielded good quality pasta. The results of the chemical composition of the flaxseed-enriched pasta indicate considerably enhanced nutritional quality, particularly the levels of protein, fat, and dietary fiber of the pasta, without affecting its quality. Moreover, flaxseed cake can be an important source of nutritional ingredients for pasta production, although it is a by-product of the oil cold pressing technology.