Papaya seeds (Carica papaya L.), a by-product of the food industry, contain primary metabolites and offer secondary health benefits, but are often considered a waste with no value. Therefore, the aim of this research was to optimize the extraction process of polyphenols from papaya seeds (Carica papaya L.) to maximize their antioxidant activity using the response surface methodology (RSM). A design of experiment (DOE) approach was applied to produce the optimum conditions of factors such as solvent concentration (0–100%), temperature (30–60 °C), time (1–6 h), and exhaustion (1–6 times) to improve the extraction process. The response variables were the number of phenols and flavonoids, and the inhibition capacity of the DPPH and ABTS radicals. The main findings indicated that optimal conditions—100% solvent concentration, a temperature of 30 °C, an extraction time of 6 h, and 6 depletion cycles—maximized the yield of total polyphenols, total flavonoids, and antioxidant capacity, as evaluated using ABTS and DPPH assays. The extracts presented values of 2.521 to 6.168 mg AGE/g DW for total polyphenols and 30.830 to 68.599 mg QE/g DW for total flavonoids. Likewise, they presented an antioxidant capacity using DPPH and ABTS methods with values of around 15.151 to 72.389 and 29.434 to 165.393 μM TE/g DW, respectively. Identification was also performed using liquid chromatography to determine the presence of sugars (glucose, fructose, and sucrose) and organic acids (oxalic, citric, tartaric, malic, quinic, and succinic). However, optimal values were presented outside the study area, which indicates the maximum point of the surface was at intervals higher than those studied in this investigation. The papaya seed can be applied in future research for the optimization of bioactive compounds extracted from vegetable waste and it represents a matrix with potential in the area of technological development and health.