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Ultrasound-assisted extraction (UAE) is widely used; however, the efficiency of extraction depends on the raw materials. Therefore, optimization of UAE must be investigated for each type of plant material. By-products from soursop fruit have not been studied as a source of bioactive compounds. In this work, the optimization of UAE conditions (extraction time (5, 10, and 15 min), pulse cycle (0.4, 0.7, and 1 s), and sonication amplitude (40%, 70%, and 100%)) for the extraction of phenolic compounds (soluble, hydrolyzable, condensed tannins, and total polyphenols) from soursop by-products (seed, peel, and columella) and pulp was evaluated using response surface methodology. The optimal conditions for UAE to obtain the highest total polyphenol content from by-products and pulp was dependent on the raw material. Peel resulted in the highest content of total polyphenols (187.32 mg/g dry matter [DM]) followed by columella (164.14 mg/g DM), seed (36.15 mg/g DM), and pulp (33.24 mg/g DM). The yield of polyphenolic content from peel and columella obtained with UAE was higher (32–37%) than conventional extraction for 2 h under stirring (14–16%). The contents of gallic acid (0.36–15.86 µg/g DM), coumaric acid (0.07–1.37 µg/g DM), and chlorogenic acid (9.18–32.67 µg/g DM) in the different parts of the fruit were higher in the extracts obtained by UAE compared with a conventional extraction method (0.08–0.61, 0.05–0.08, 3.15–13.08 µg/g DM, respectively), although it was dependent on the raw materials. Soursop by-products can be functionally important if they are used to extract bioactive compounds by UAE; a technology with high potential for commercial extraction on a large scale.