Simple Summary: In recent years, confined pheasant farms have been gaining popularity in both stocking and the production of meat and eggs. When assessing the nutritional value of meat products, the focus is on the nutrient content, including the mineral content and the amino acid profile. The production performance, e.g., body weight gains, feed conversion, and the proportion of meat in the carcasses, are also not insignificant. At the same time, taking into account the feeding behaviour of pheasants, especially during the rearing period under farm conditions, varied dietary components are used, including meals of animal origin and mineral-and-vitamin supplements. The authors hypothesised that the introduction of insect meal to the diet, instead of plant protein feeds, would have an effect on the production performance and the nutritional components of the muscles. The study results obtained show that the addition of insect meal contributed to an improvement in the meat yield and the levels of certain minerals without significantly affecting the amino acid profile. A 20% addition of meal from the larvae of insects Hermetia illucens proved to be most beneficial. Abstract: The aim of the study was to determine the effects of replacing soybean meal with insect meal on the body weight and the chemical composition of selected muscle groups of common pheasant females and males, including the mineral composition and the amino acid profile of the thigh and breast muscles. The study was conducted on three feeding groups, namely one control and two experimental groups. In the control group, plant feed components were used, which are commonly used to feed pheasants in confined breeding facilities. In the experimental groups, 100 g (group II) and 200 g (group III) portions of insect meal were introduced instead of the plant-protein components. The experiment used a preparation of insect larvae (Hermetia illucens) containing approximately 52% crude protein. The pheasant diet supplementation applied contributed to an increase in the proportion of muscles in the carcasses, with the highest effectiveness obtained for a 20% addition of insect meal. Lower and significant differences were noted in the feed conversion by birds from the experimental groups, as compared to the control group. The chemical composition of the birds’ muscles also changed. The experimental groups exhibited higher protein and fat contents and a lower water content. No significant changes in the amino acid profile or the mineral composition of the muscles were noted. The few exceptions concerned the methionine levels in both muscle groups and the isoleucine levels in the breast muscles. In most cases, the mineral composition did not vary significantly (p < 0.05). When supplementing the diet of breeding pheasants for improving meatiness, a 20% addition of insect meal is recommended, which affects the production effect of this trait while reducing feed consumption and maintaining the fatty acid profile.