Existing food trends and modern consumers’ nutritional preferences have led to a rising demand for plant-based sources of protein such as hemp seed meal and the possibility of consumption hemp-rich products, most often in wheat-based staple foods, such as pasta. Pasta, as a conventional food product, is widely consumed worldwide due to its nutritional value, long shelf life, easy preparation, versatility of uses and also relatively low cost, which has made this product popular over time. Five formulations of rigatoni-shaped pasta obtained by partial replacement of wheat grain flour with 5%, 10%, 15% and 20% hemp seed meal (HSM) were studied regarding the technological, physicochemical, textural, antioxidant and sensory properties of the pasta samples. The substitution of wheat flour with hemp seed meal (HSM) led to a slight increase in the cooking loss (CL) and optimal cooking time (OCT) compared to the control sample, while the water absorption (WA) and swelling index (SI) decreased during evaluation. The experimental results also showed a decrease in luminosity and fracturability, with an increased firmness of pasta dough. Moreover, the developed pasta showed a significant improvement in antioxidant capacity in terms of total phenolic content (TPC) and antioxidant activity (DPPH). The pasta samples with 15% and 20% HSM substitutes experienced a browning process due to the Maillard reactions during drying, as well as a color loss during cooking; however, the color changes did not affect the acceptability of the product. The partial replacement of wheat flour with hemp seed protein highlighted the possibility of developing a new innovative type of pasta that claims a functional benefit and presents an improved nutritional value, mainly due to the partial protein intake, as well as certain benefits for a human diet.