The study aimed to analyze gene expression linked to skeletal muscle growth and lipid metabolism in broiler chickens fed with plant extracts. Five groups of chickens were formed: four experimental groups and one control group. The diets of the experimental groups were supplemented with different plant extracts: chicory, St. John’s wort, maral root, and creeping thyme, whereas the control group received feed without phytobiotic compounds. Weekly weighings were conducted (n = 36). The chickens were slaughtered at day 26 for tissue sampling of four birds from each group. Gene expression (MYOG, MSTN, FASN) related to muscle growth and fatty acid synthesis was analyzed using the β-actin ACTB gene as a reference. Blood samples were taken at day 35 for biochemical analysis and anatomical dissection was performed. The study revealed that using plant extracts from chicory, thyme, and maral root increased MYOG gene activity by 4.21, 7.45, and 8.93 times, respectively. T. serpyllum extract boosted the MSTN gene by 10.93 times, impacting muscle growth regulation. FASN gene expression for fatty acid synthesis increased significantly by 18.22–184.12 times with plant extracts. The best results regarding meat productivity of chickens were obtained when using R. carthamoides extract. The results of the study will serve as a basis for further development of a phytocomposition designed to increase the meat productivity of broiler chickens in the production of environmentally safe poultry products.