Stinging nettle (Urtica dioica L.) is a good source of biologically active compounds with proven beneficial health effects. This study aimed to investigate the effect of nettle herb supplementation on chemical composition, including the content of selected minerals and pigments, the in vitro glycemic response, and the cooking and sensory quality of extruded pasta. Tagliatelle-shaped pasta was produced under semi-technical scale by partial replacement of durum wheat semolina with 0, 1, 2, 3, 4, and 5% of lyophilized nettle. The partial substitution with freeze-dried nettle caused a statistically significant (p ≤ 0.05) increase in the content of minerals, especially calcium, iron, potassium, and magnesium in the products. The calcium content in the pasta fortified with 5%-addition of stinging nettle was 175.9 mg 100 g−1 and this concentration was 5.8 times higher than in the control sample. At the same time, high content of chlorophylls and carotenoids (237.58 µg g−1 and 13.35 µg g−1, respectively) was noticed. Enriching pasta with a 0–5% addition of stinging nettle resulted in a statistically significant (p ≤ 0.05) increase in the content of the total dietary fiber (TDF) (from 5.1 g 100 g−1 to 8.82 g 100 g−1) and the insoluble dietary fiber (IDF) (from 2.29 g 100 g−1 to 5.63 g 100 g−1). The lowest hydrolysis index of starch (HI = 17.49%) and the lowest glycemic index (GI = 49.31%) were noted for the pasta enriched with 3% nettle.