The effect of the extraction conditions on the DPPH radical scavenging activity and isolation of bioactive compounds from the maca (Lepidium meyenii) root was investigated. Different extraction techniques (maceration, maceration with shaking, ultrasound-assisted extraction, and reflux extraction) were compared. Moreover, the effect of the extraction time and two various solvents (water and ethanol) was studied. The antioxidant activity of extracts was determined by the spectrophotometric method with the DPPH radical, while total phenolic content (TPC) was analyzed by the Folin–Ciocalteu method. Using gas chromatography with a mass selective detector (GC-MS), some characteristics of maca bioactive compounds were identified in the extracts: benzylalkamides (macamides), sterols, nitriles, fatty acids, and their derivatives. The influence of various factors on the extraction process of health-promoting antioxidant compounds from maca root was discussed. It was found that water was a more effective solvent than ethanol for obtaining extracts characterized by high radical scavenging activity and phenolics content. Nevertheless, some ethanol-extractable valuable compounds specific for maca, e.g., macamides or fatty acids derivatives, were not present in water extracts. In developing nutritional and therapeutic formulations based on maca extracts, it is important to take into account that the bioactivity of maca extracts varies depending on the solvent used.