This study aimed to optimize the extraction of phenolic compounds (PC) and the antioxidant capacity (AC) of Inca muña by conventional solvent extraction (CSE) and ultrasound-assisted extraction (UAE). Optimization was performed by response surface methodology. CSE evaluated variables included EtOH (%), temperature, and time; UAE evaluated variables considered amplitude, time, and EtOH (%). Optimal CSE parameters were EtOH (46.3%), temperature (68.7°C), and time (62.7 min), while optimal UAE parameters were amplitude (70%), time (8.9 min), and EtOH (70%). UAE was more efficient achieving a higher PC extraction (10.4%) and higher AC (27.2%) with shorter extraction time. Thus, under optimal conditions, values of total phenolic compounds (T-PC) and AC of 182.2 mg GAE/g and 1,470.0 µmol TE/g, were obtained. The extract was mainly composed of chlorogenic acid (isomer) > rosmarinic acid > eriocitrin > naringenin. The extracts obtained are an alternative for various industrial applications. Practical applications: The Inca muña is an aromatic plant of Andean origin widely used in traditional medicine. Inca muña leaves contain a large number of phytochemicals including phenolic antioxidants, essential oils, iridoids, sterols, diterpenoids, among others. In this work, the extraction of phenolic compounds and antioxidant capacity has been optimized using conventional solvent extraction and ultrasound-assisted extraction (UAE). With both technologies, extracts with a high content of phenolic compounds are obtained, with the advantage that UAE allows to obtain better results in less time. Extracts with a high content of chlorogenic acid and rosmarinic acid were obtained. The extracts obtained from Inca muña are an alternative for the development of functional foods, nutraceuticals, and for other industrial applications.